I grow stone fruit trees and use various products to protect them. Rust is not a problem here. But last year I bought a tree with it, and it soon spread to all my figs. When figs are actively growing and infected, nothing is going to work well. The time to eradicate the problem is when dormant. I spray my dormant stone fruit with a strong copper spray, which is very effective with leaf fungi problems including leaf rust, leaf spot, and leaf curl on stone fruit. It is a preventative, not a cure. So in the fall when leaves dropped or in late winter/early spring I spray. I sprayed figs this spring with copper, I used a commercial copper that is much stronger than consumer grade copper, I also use a commercial sticker (Nu Film 17). The copper I use is copper hydroxide which is much more effective than copper sulfate.
I'm confident the rust will not be back. The figs are fine and all starting to wake up now. You could try a copper sulfate while growing, but I would test on a throw away plant first. Lime Sulfur is another product that will probably work too. It is not easy to find, and should also work. Spray plant and soil around plant.
Use at own risk, as stated no fungicide is approved for figs. One reason is testing plants is very expensive and few people grow figs so the chemical companies feel the cost to get approval on figs is not worth the expense. I have no doubt these products will work. The rust doesn't stand a chance. Again though you must use when dormant and no active infection is occurring.
Copper does not appear to hurt the fig trees if proper amount is used. Using too much could kill an actively growing tree (no chance if dormant). Sulfur could too, you have to test!