I don't know where you live, but I'm wondering about the humidity variable. The higher the humidity, the longer it will take for this stuff to dry, and even then, it may still feel a little sticky on humid days. I had trouble with my first two coats because I hadn't stirred well enough and there was too low a percentage of solids in the mixture that went on the floor. So it wasn't drying, and in fact leaving an oily film over everything. Your problem is a little different, but perhaps you can try what worked for me and see if it helps. First, I'd opt for getting some air MOVEMENT over the floors, as opposed to "airing out the house." Get several large fans that can really move a lot of air and set them so they blow across the wood. Set one up in a window, also, blowing out of the house--this will draw the fumes and push them outside. Leave it like this for at least several days. Second, I don't think digging into the layers to check what's underneath is a very productive thing to do--you'll just leave yourself with a patchy finish that you'll have to try to fix. That will mean applying MORE poly, and you already have too much down.
I think it might be possible to salvage this, but only if you think carefully before doing anything more physically to the floors. You have to expect this will take a much longer time to cure, if it's going to at all. In the meantime, you can't be putting rugs, furniture or feet on these floors. So I hope these aren't rooms you absolutely need to be in to get around your house.