I'm restoring an old garden; it is a lot of fun. There is a big old grapevine which has turned into an impervious mat of dead and live vines and various weeds and saplings. It is growing on and through an open-weave fence, and the whole thing is probably three feet wide by now. The fence has probably collapsed inside. How would I proceed? Fruit production does not have to be optimal.
Probably cut off dead vines. Check on fence's structure, maybe make a new one. Then train new growth up it. I wouldn't keep the large vines, you probably can't train them at this point. Anything woody should be cut off or trimmed for new shoots.
I think you should maybe cut it down to one central leader.
I have done this with my vines, and they just come roaring back.
Now I have it trained along a cable spanning the north wall of the house, and I'm letting branches grow down from there.
Even though it will swine and grab, I tie it in place, to give me more control.
If the fence is metal, you might be able to burn off the growth, and recover the mesh.