I grow figs, and you can prune hard no problem. I do agree that the only way to fix the lean is to dig it up.
It’s a great time for you to do this too. It’s dormant
Do shape the tree too. You need to prune to get it to grow the way you want.
The main crop is on new wood only. The breba crop is on currant wood. If your tree even has a breba crop? Not all figs produce breba. So the wood your largest crop is on has not even formed yet. What’s fantastic about figs is they grow so fast it’s easy to reshape, even regrow a new main trunk. I have done this many times as damaged wood needed to be removed. On a couple trees, a small sucker from the base was picked as the new central trunk . The main trunk was then completely removed. The plants are fine. Doing great! I did lose the crop for a year or two, but I have so many trees, I don’t really care. I would rather have the tree shaped as I prefer. So cut away. You could lose a year of decent harvests, but removing no more than 1/3 of the tree should not change harvest yield that much. So over a few years you can reshape tree. When you prune the tree that will stimulate new branches and suckers from the base to grow. A side effect of pruning, so one must keep on top of these trees with regular pruning to maintain structure.
What I do is grow most in tree form. They can be grown as a bush too. Anyway I try to form 3-5 scaffolds. Once fully formed fruiting branches form on the scaffolds. Once done the fruiting wood is removed, leaving 1-2 nodes. Much like cane pruning on grapes.
