M. Polter, with all due respect, you did everything wrong. Sure would have loved to talk to your before this project so that all of this would not have happened.
Without allowing each layer of poly to properly dry before another coat just made the floor like syrup or jelly. Each coat could not dry because there was another ontop of it before it could cure out.
What you need to do is allow all of this to fully dry out and then begin a more difficult task of taking all of this off and starting over. Poly, as much as you stated, is one tough dude to sand. It tends to just gum up the sand paper quickly and its just a mess.
Lets see if some one else has some ideas on some sort of stripper that could get this stuff off quicker. The use of a stripper in the house would be the smelliest thing that you have ever done. I am not sure this is the proper way to go.
Before you pay someone to come out and remove this, lets be sure that this person actually knows what they are doing. Do some research on this before committing to a contractor.