If there are enough shoots,maybe try cutting some and growing them.There are videos on how to on Youtube.Brady

I would dig it all out and start over with a new plan. It sounds a bit unruly and who knows what the end result of your salvage project will be. The tree is suckering which can make it a "weed" of a tree.

Besides, once fig trees are established they are like tanks. Something had to have gone terribly wrong or someone tried hard to make it go wrong. I don't like either scenario.

Even if you dig it all out, I wouldnt be surprised if it still came back from a chunk of root you missed.

My main concern is how do you know the fruit will be good? If you feel sure it is a good eating fig, I think you can revive it. I am growing Brown Turkey here for 20 years with no summer water. My soil is clay loam with average winter rain of about 30 inches. I am also 'blessed' with numerous wild figs growing throughout my garden, being removed yearly. I let one grow to see if the fruit was usable, and found it was not. Al

You mention rootstock. Figs are normally grown own root, meaning they aren't grafted onto a rootstock. Your fig is probably own root, therefore, I would not prune it, but let it grow.
Figs like a lot of lime, so I would lime the tree, and keep it well watered and mulched.