I was in a similar situation once, but mercifully on a much smaller scale. We had an Evil Contractor(tm) who had worked most of his way through a project, but things had turned very nasty and he had to be escorted out of the building by security. So there wasn't exactly a lot of opportunity for handover, you might say.

In this case, it was easier to actually start from scratch, and build the thing in about four weeks (the Evil Contractor had been there about three months I think). Amazingly, the end result actually worked, and the product was sold on to another company, marking one of my proudest working moments :)
Anyway. I don't envy you one bit. Sounds like a horror. I think the first thing I'd do is get the implemtation date changed. Basically, lots of 'expectation management' required. The sad thing I guess is that you'll probably need to spend a fair bit of time covering your own arse to make sure none of these stuff-ups can be attributed to you.

Or shift the onus back on managment - get them to make the 'fix it' or 'rebuild it' call, based on your estimates of how long each would take. But I guess, make it abundantly clear that neither would be possible by Jan 1.

Anyway, guess I've just made it abundantly clear I know nothing about project managment. But the very best of luck all the same! :)