A pva adhesive (white or yellow does make any difference, as the color is just an additive) requires a glue line of 0.002" to 0.006" thick. I wonder if you center area is perhaps a bit too thick and that is why you do not get a cure in 24 hours. The role of pressure is to smooth the thickness of the adhesive and to squeeze out any excess amount. With a large piece, you will have trouble getting the excess adhesive to squeeze all the way to the outside.
Pressure does not squeeze the glue into the wood cellular structure. So, if you surfaces are perfectly flat, you might have to use less spread int he center or maybe make a reservoir slot in the center area to hold the excessive glue. Of course, pressure is the key...not too much but not too little either. As you are used to epoxy which does need a thicker joint, when switching to pva, you will need more pressure than with epoxy. (Once the pressure is applied, do not let it be reduced, as that wood will then spread apart and there will no longer be enough glue to fill the gap...you squeezed the excess out already.
You can increase the temperature a bit to encourage the moisture to flow away and the joint to cure...maybe 80 F. It does not need oxygen to cure. In fact, the dry wood should be able to easily absorb all the excess moisture so the joint will cure
If the joint thickness is OK, how could the moisture stay in the center if the wood was dry? The only way I can imagine is if there is a lack of pressure (or a large gap over 0.006"). Epoxy does fill a gap and stay strong, but not pva adhesives. (I hope that your wood surfaces are perfectly flat and not hollow ground, as we sometimes saw in the past.
Note that a good pva joint will be 50% stronger than the wood itself, so epoxy is not needed in a simple joint where the surfaces are flat.
One other thought is that your surfaces may not be active for gluing, due to age, heating, etc. Put a drop of water on the surfaces to be glued and see if the drop soaks into the wood within a few minutes. If not, you need to have a better surface for gluing. I can discuss this further if needed.