Over the years I've learned that problems are ever rarely as bad as they seem. Indeed, going into a panic can often make a simple problem oh so much worse.
Case in point - I was putting the first coat of poly on 4 of my puzzle boxes yesterday (would have been Saturday morning). That finish is supposed to dry in 4 hours. Saturday night, still tacky and that was after setting a low fan on the pieces.
Panic was starting to creep in. But I've been here before. Finishes often don't dry in their advertised time frames. I waited till Sunday morning - better, but still a bit tacky. So I put the pieces out in the morning sun for a few hours. Brought them in around noon - still a tiny bit tacky, but definitely better. Set the fan on them again and waited another hour or two.
Much better - plenty dry enough for the next coat. The slow drying may cause me to do a bit of extra sanding as I likely got some dust nibs, but that's far from the end of the world.
What could I have done in a panic - tried to strip the finish off and likely damaged all the boxes. Since they are all wood burned, glued up and oiled, I could have completely ruined them. Instead, sit back, wait a bit and see. Go online and read about different types of finishes, drying agents, temperature and humidity issues. While you are doing that, the finish will likely dry and you'll be more experienced for the next time.
Why did it dry slow? Not quite sure. It's an older can of finish, that could be the problem. Maybe I wiped it on a bit heavy and that slowed it down. Maybe it was a bit too cool. Maybe it needed more time over the existing oil (even though I know the two are compatible). Hard to say for sure. Maybe it was all those reasons.
Now I'll wait for the second coat to dry and try not to panic.