Is there some way that the Paster can be made aware of the special situation you are all in? The fact that not only will you have no place to stay, and not only are you pregnant, but the baby will be pending birth at any moment under that schedule. Perhaps you can guilt him into making a comprimise. 3 weeks / 3 weeks sort of thing. So you get in a little early and he's out a little early.
It would be easier for him to be in a hotel room wouldn't it? Maybe he would be open to the hotel room option more so that you are?
I hope it all works out for you. Heck - what am I saying? It will work out. Everything happens for a reason. This is all going to be okay.
