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Thin your poly with mineral spirits if you want, or don't. Doesn't make a difference in adhesion or drying in this situation. It just makes it easier to wipe on. Use that acetone, instead, to thoroughly wipe the wood
before you apply your finish. You may have to wait a few hours to days before you use the acetone again. You're trying to wipe away the surface oils of these naturally oily woods before that poly finish gets on there. With the oils of these woods gone (at least at the surface where it counts with this type of finish), the Poly has a place to stick and hold.
Are these pieces being stored in the cold to dry? If so, it's going to take awhile to dry and become hard regardless of what you do. A warm environment speeds things along.
Now, how to fix the problem at hand? You can wait for a few weeks to see if that Poly finish hardens up. Considering the holiday season is fast approaching, that's probably not an option. So, strip off the Poly finish with some mineral spirits and redo with the above instructions.