I am not recommending anyone else do this, just telling what I did and showing some of it. If you can't do this or don't think it is a good idea, get some professional repair help, or better yet, buy new boots!
A few years back I replaced my Mogema and my beloved Verducci V-Tec boots after deciding they were too far gone to fix. Believe me. If I can't dream up a fix (whether or not it would work) they really are toast.
Many of my repair dreams involve various types of epoxy (either the two-bottle, dual-syringe, two-tube or the single-tube-of-putty sort made like caramel creams, e.g. waterweld) plus various "found objects" like used USPS Tyvek envelopes (as it's not nice to use the new stuff, ya know?), various kinds of plastic sheeting, air sole material, stuff like that. (Tyvek layers epoxied on can make a decent patch to strengthen some weak carbon spots, in my opinion.)