A previous answer doesn't answer my question. I have a similar situation with a new house and long neglected vines, except with my vines, there was no trellis, and the vines were growing high into the trees. I probably have 25 feet of thick old vine before there is any new foliage. 

How drastically can I prune these old vines? 

I decided to build an overhead trellis that I can walk under rather than a fence type, (but I'm not sure now if my idea will work right now that I have done more research and reading). 

Any suggestions?