OK, I did not read the whole question, only the highlited part befor throwing in the response below.. Just ignore it.
First question would be who dictated the revised close date? The banks like to force (or try to) everyone to do things on their terms. They probably had some "higher up" tell them to get it off the books this month, thereby shortening the close date. Their leverage will be that they can only approve the deal if that is when it closes. If they do your options are to tell them NO, you would rather have the 2 weeks and they can take a hike, or figure something out and get it done when they want.
It is really too bad the buyers are being sticklers on renting the house back, but I understand their not wanting to become impromptu landlords.
Feel free to contact me off the forum if you want any more info. AND keep in mind that Real Estate Licensees cannot give legal advice. You may want to contact some council regarding the legal standing of your position.
Let me know if I can be of any more help.