I am looking for conceptual suggestions for a jig I need to design to help me quickly cut (in volume) a 1/4" x 1/4" lengthwise groove down the center of an 16" work piece. Currently, I am doing this using a very time consuming manual way.

With a rectangular piece this would be a piece of cake. However, 3/4's of my 16" workpiece is tapered on all four sides, but the bottom 4" is not tapered. Picture a 12" high 4-dimensional pyramid that sits atop a 4" high cube. To get a straight and centered groove down the full length of the piece I need to compensate for two issues during each pass-through. One, the gap created (during each cut) between the tapered side facing the fence and the fence itself. And two, as the dado blade completes its cut on the 12" taper I need a reliable way to push down on the bottom 4" of the workpiece--off the table 1/2" or so up to this point--to bring it into contact with the dado blade. This last part is always a scary moment, not from a safety point-of-view but just in terms of making sure I don't move the piece off-center as I push the piece through the cut. Any ideas would be appreciated. I don't expect anyone to actually design this jig for me. And I am well aware that this may just be too detailed a situation for anyone's comment. Thanks.

Use a 1/4" piece of plywood 8" wide over the top of your work piece aligned with the center of your part. For volume work I'd index the 1/4" part to the work piece and then glue a sanding belt to the underside of the 1/4". using a power feeder will apply the pressure needed and feed the part. the sandpaper will keep the 1/4" "jig" in alignment with the work part and be fed thru the saw.

Bruce H. thanks for your input. Your idea sounds intriguing but I'm having a hard time visualizing it. You suggest 1/4T x 8W ply but what length? How do I index the ply? I know the concept of indexing but don't see how to apply it here. What rides against the table saw fence to keep everything in line as cut is made? And what happens when bottom 4" x 4" x 4" (not tapered) is reached? How is a clean push-down (to the table) of that part executed? I don't have a power feeder so this is all manual.

I'd make the pattern a couple of inches longer than your part. Index it down the center of your part either with a drawn line or attach a piece that your part butts into.

the 1/4" piece rides against the table saw fence, your part is suspended under the pattern. I suggested 8" wide because you said your part is 16" wide so the edge would be down the center line.

you could hand feed this however a feeder would be a wise investment, in terms of speed, accuracy and safety.

Can you run the dados on the radial arm saw? Make two separate jigs for cutting the different planes. A jig for this is simply an indexing fixture to hold the part in place while you cycle the radial arm saw.
If you're stuck with the table saw, I'd still use two passes, one for each plane of the cut. The jig here, is a sled with a bridge across the front and back so you don't cut the fixture all the way through the first time you use it. The "bridge" pieces are dead square to the miter slots and act as fences. Make them tall enough that the piece still engages when the triangle plane is down. The workpiece rides against the saw's rip fence for finding the center. Two passes, if all your parts are perfect, your dado blade is wide enough, and you can dial in the exact center. Or, do it with four passes (two against each "bridge") to hit the exact center with any inconsistency varying the width of the dado.

...and next time, try doing your machining before you make the tricky shapes.