I recently read an article about a man "cloning" pumpkins. The idea is really simple. As you may or may not know pumpkins grow secondary roots at the base of each leaf node. What he seems to be doing is simply burying the vine in a separate pot when the vine is around 2 feet long and leaving it that way for about a week. By then the secondary roots should begin growing and you can actually separate the two plants by cutting the vine just before where you buried it in the second pot. I have never tried this but it is the only thing I can think of to keep the plant going over winter. You will need some decent size pots you might only be able to grow 5 or so plants like this.

Also to keep yourself from collecting more and more plants over the winter you might want to consider only saving the plant with healthy strong growing tips. What I mean is that when you do the "cloning" you could discard the older part of the plant and keep the recently rooted healthy tip. Below is the link to the original article.

Pumpkin Cloning

If you do try this method I would be interested to hear how it goes over the winter.