The problem with air dried woods is that there will be a differential moisture content between the surface and the core. By opening up one surface when routing along with the spindle fan blowing warm air on it while routing for a few hours you are force drying that one face only.
I would think about doing a pattern of relief cuts on the back of the panel immediately after routing the face. I have done some signs from 1 1/2" thick cedar. They cupped somewhat after carving the first side. After carving the second the cupping was minimal.
It is always a good practice to acclimate wood in the shop before working it kiln or air dried. Particularly air dried in winter when the relative humidity is lowest.
Kiln dried lumber will cup if only worked on one side as well depending on species, flat or rift/quarter cut and the skill of the kiln operation.
Your best bet would be rift/quarter cut , kiln dried wood with sufficient thickness that will allow you to skim cut the back to balance the stress relief on the back.
Be careful to cover the freshly cut face when not working on it. Don't expose it to strong sunlight or heaters.
You will do best to finish the front and back the same. Same finish ,same number of coats. Wood movement is the most extreme in the first seasonal swing of humidity. With each subsequent year the shrinkage is decreased for a few years.
By the way, that is a very clean carve. I'm impressed. What is the size?

That is nice work, and a shame that you are having problems.

Before I can give my best advice, I would like to know how or where it was displayed? Hanging on a wall, laying on a table, or hanging on a frame with plenty of air circulating on the back?
How many boards were glued up, and not only which side was the pith / bark? How steep or flat were the rings on the endgrain?

@Tom Gardiner Thank you for your observations. The model showed no cupping after cutting in the shop; it only developed at the customer's house a few days later. I imagine it would take weeks if not months for air-dried wood brought in to a heated shop to reach the same relative humidity. Rather, my goal--when I can reach it--will be to stick to kiln-dried, and if required to use air-dried, to cut-both-sides-equally.

The largest of the 3, "mostly identical," models is about 20"x18"x1", which reminds me of another goal: nothing thinner than 1-1/2" _and_ carve to <50% depth. Incidentally, I use just 2 carbide cutters: 1/2" endmill rougher and 1mm roundnose finisher, with 1/4mm stepover per pass.

@Keith Newton You put your finger on it immediately. As the farmer suspected, displaying it on the wall exacerbated the cupping by restricting the air flow to the back side. That fact actually leads me to believe now that there is no way I'll be able to protect against cupping. Even with both sides cut _identically_--unless there is no moisture exchanged--the side against the wall will necessarily dry slower. I think the best bet is to flatten it, clamp it, and let it dry in-the-house for-a-long-long-time. That goes back to Tom's suggestion: how long does it take air-dried would to acclimated to conditioned airspace?

There were four or five boards making up each blank. Farmer had ripped-and-flipped boards before gluing to minimize cupping, we thought. It turns out that cupping due to endgrain tendencies is dwarfed by cupping-towards-the-cut-side. To answer your specific question, neither of us deemed any of the grain "steep."

Thanks for your thoughts.

Just so you know, I think your adding moisture back to the face was a mistake. That is only a temporary solution. The old common suggestion that laying a newly cupped board out in the grass cup side down in the Sun is only half right. When the goal is to get from air-dry 12% to 6-8%, laying the same board out in the Sun on sawhorses with the convex side up, will accelerate that side drying faster than the down shaded side without having to bring it back up. If the RH is low, and midday sun, may only need an hour to flatten it. It is better to do it intermittently than going too fast, which could cause checking.

Buy a moisture meter if you haven't one already. Even the inexpensive pinless meters are pretty good for what you need.
If your clients want you to work with wood they supply then you can specify that they will have to wait until it has reached an appropriate MC or advise of the risks.
I don't know if this works but you might be able to devise a wall mount that incorporates some stand offs to give the panel some air movement on the back. A french cleat up top and stand offs at the bottom.

I was thinking of suggesting the standoffs also, after drying the backside to bring it back to flat before you carved the back, AND maybe screwing on some steel reinforcement across the back, like maybe 3/8" x 1" with slots or oversize holes on the ends to allow movement.
But. now that you've routed the back, I don't know how much you have left.
Is it safe to assume from the legend that some of the numbers are for hunting stands?

I would suggest in the future to make sure the wood is thick enough to put a batton on the back side. The C channel below would be perfect for this type of thing. The thick ness of the ears will pack it off the wall for air to circulate, and the slots will let it expand and contract.

To me , it does not matter if it is air or kiln dried, it should have been properly acclimated before milling.

Also, being a farm tree, it could have had internal stresses beyond your control such as wind riff. Your cutting half way through the boards may have unlocked it.

I would also suggest for the glue up to have all growth rings oriented the same way. I feel it’s easier to keep flat that way.

View higher quality, full size image (750 X 1334)

I'm convinced now that if the moisture content of the wood is at equilibrium with the display space there will be no moisture flow at all, and thus no differential moisture flow resulting in cupping.

https://www.woodweb.com/knowledge_base_images/zp/equilibrium_moisture_
content.pdf

BEFORE hanging it against a wall, or displaying it lying flat on a table for that matter, it is imperative that equilibrium moisture content has been reached so moisture transfer will be negligible.

It will be best then to have near-equal surfaces on opposite sides with the piece in a vertical posture away from obstructions in the display space where moisture can travel relatively equally from those sides.

What you said is correct, however you also need to plan for the relative humidity changing, there by making your wood MC change as well.
If a board has a lot of curve to the growth rings, and you have a shift of 6-8% MC, the bark side will expand considerably more than the pith side, causing cup. I live in an area with hot humid summers and long cold winters. Wood movement needs careful consideration.
On another note, was your project finished? That will help slow the exchange of moisture.
Last, that map is really cool! I have always wanted to get a small cnc and dink around with it, to make things like that. What type of cnc and program did you use? Was it complicated? Thanks

NB For what it's worth, post editing is broken. After the first edit, formatting was destroyed. An attempt at a second brought up only the last paragraph.

@Keith Newton The legend identifies trails and features. I was opposed to it initially, but it will make the piece more meaningful to future generations.

I addressed, if not perhaps resolved, the problem of cupping towards the carved side in wet wood by creating roughly equivalent surface area for moisture transfer through the opposite face. A composite picture showing opposite faces and edge is attached.

Here are my final thoughts, offered for a future carver who may end up here.

Imagine that a digital model to be cut is represented by a black-and-white and non-uniform image, with coincidentally a white (full-height) spot somewhere near the left edge and a black (full-depth) area near the right. Assume the model is to be cut from 1" stock with white at depth 0" (the top surface) and black at 3/4". At its thinnest the resulting carving will be 1/4" thick and a full 1" at its thickest.

If the equilibrium moisture content (EMC) of the wood is consistent with the relative humidity (RH) of the environment, no moisture transfer will occur, and the wood will not cup.

When the relative humidity changes, moisture transfer will correspondingly take place, and to the precise extent that it will occur more readily on one face than another, the wood will have a tendency to cup towards or away from the face with more area. If the RH goes down, the wood will dry and the carved face will dry faster and the wood will cup towards the face. If the RH goes up, the carved face will swell and the face will bow.

If however, the back of the model were carved in a way that provided equivalent area--for example, having the equal-but-opposite carving--the moisture transfer rate will be equal (ASSUMING there are NO OBSTRUCTIONS--such as a WALL or TABLETOP), and the cupping tendencies will be reduced.

When the board is flipped, the edge with the white/high area will be on the right and the one with black/low will be on the left.

The black-and-white digital model must be flipped left-to-right to ensure the white and black areas align. (Imagine the digital model is a series of alternating black and white bands of different widths with a 45-degree slant, NW to SE; the digital model must be flipped to match both the slant and the widths.)

However, although the areas now align, if carved this way, the result would be that white would be carved over white resulting in an overly thick area in the carving and where black is over black the model would be thinnest--and might even be cut through.

If the gray levels of the reversed digital model are inverted before cutting, such that white becomes black and vice versa, the result will be that the deepest cuts (i.e., black areas) are cut over white areas on the opposite side (the shallowest areas of the original). If the reverse-inverse digital model is cut to the same depth, the carving will also be of uniform thickness, 1/4".

Carvings are typically made with two passes: a roughing pass with a relatively larger cutter followed by a finishing pass with a finer one. It is not necessary to carve a perfectly faithful equal-and-opposite model, although that would be ideal. The goal is to approximate the surface area of the carved side.

This is done in two steps.

Firstly, use CAM software[1] to generate a standard roughing pass calling for using a large-diameter cutter, but with non-standard parameters. For example, in cutting the normal model, a 1/2" endmill might have been specified with a 0.1" depth-of-cut and 0.1" stepover and to leave 0.01" remaining.

For cutting the reverse-inverse digital model, the specifications might be for 0.25" DOC and 0.5" SO.

The second step is to execute the roughing-pass program using an endmill of half the diameter specified. This will result in channels--which will have higher-surface area--being made.

Assuming that the carved model with equivalent-area-faces dries uniformly to match the environment with no cupping, the relative humidity in the environment will still change and if air flow to one face is obstructed, the tendency to cup or bow will return. Wood finishes are applied to address this tendency and to a greater or lesser extent slow the moisture transfer, to stall it, say, until the prior environment returns.

There's a Master's thesis here to calculate precise parameters to compensate for any carving.
[1] I'm a long-time MeshCAM user. It is no longer sold, but alternatives abound.

View higher quality, full size image (4160 X 2340)

Equalizing moisture transfer by creating equivalent surface areas on opposite faces can mitigate cupping in carved wood. Reversed and inverted digital models, along with modified CAM settings for roughing passes, help achieve uniform thickness in carvings. Wood finishes can further regulate moisture transfer.