My $0.02 worth...
I'm looking at the Homeway sights (VRBO, CyberRentals & HomeWay.com) but everything is gone or extremely expensive; any other suggestions?
You might want to be a bit more specific about your personal location priorities. Bear in mind that there are six different individual states
here in New England (....although I personally advocate giving Connecticut away to the New York area, thereby reducing New England down to five
states and simultaneously having CT become more appropriately "affiliated").
Keep in mind that New Years' is both the tail end of a school vacation week
and is also prime ski season as well. Combined, those factors put lodging at a premium in many NE areas. If it's NYE revelry you seek, Boston's First Night can't be beat (but good luck finding any available accomodations).
One site you did not mention having examined is vacationRentals.com. I'm certainly not endorsing (or advertising for) the site --- I'm just pointing out that it's one you may have missed in the course of your lodging quest.
I'm not even going to ask why you would want to be in New England instead of in the Bahamas in January --- the scenario brings to my (alleged) mind an old movie with a "Jamaican bobsled team". Good luck.