Established grapes do not transplant well, but if you get enough of the root, you may be successful. They have a very extensive tap root and so it will be difficult for you to get all of it. The more, the better.
It will not store well over the winter, so it is best to re-plant it as soon as possible.
Grapes can,(and should) be pruned back very hard each year, so I would suggest that you cut away most of the secondary growth, transplanting the main trunk and a limited number of smaller branches. Water it well until freeze-up and through next spring and summer until it is re-established.

Ian

How did it work out? I transplanted some concords when I adopted 3 vines at the same time you did a few years ago. There was a large tap root to work with and they all died, I didn't know til spring. Even though it's late, I would prune way down so it can concentrate on the roots. I would also visit them often and touch them often to give em good energy. I would also make sure they have lots of compost, and mulch so their roots are happy. I would also save some branches of the pruninga and put in the soil for new vines in case they dont make it.