What's the flooring like in the area that's squishy? Could you hire someone to remove the flooring from that area so that you can look underneath and see what's wrong? If it's wood or linoleum that shouldn't be too hard. Tile would be tough. Maybe contractor 4 could do this if he comes back to look under the house? It could be something as simple as cracked or rotted subfloor or it could be a foundation issue.

To me, the fear that it could be the foundation would be good incentive to look at licensing options out of state and/or take another look at rental options in your area. In terms of rentals...have you asked friends and family if they know anyone with a rental that may work for you? Maybe put some feelers out and see if anything comes up. As others have said, now would be the best time to move on from a troublesome house since the market is so hot. Buyers may be willing to overlook issues that they won't in the future.

Also...I would never contact contractor #2 again since throwing out a figure like that w/out much info seems wrong to me.