Will these types of pots work for cooking gumbo?
As for working, they will certainly work. A cook can learn to use pots with irregular heating patterns. 

The bigger problem is, can you work with large pots? If no, then your plan won't work, independently of the pot thickness you choose. A pot of this size just doesn't behave like a small pot. It will have a heat gradient vertically, and, unless you have a giant paella burner, also horizontally. And this will happen even with the best bottom. Also, if you are making roux by one of the "depends on speed" methods, the sheer amount of roux and liquid mean you won't be able to mix before lumps form, and you may suddenly find yourself in need of more hands when you realize you can't lift your prepared liquid one-handed. 

If you are confident that you can deal with that, then the pots will do all right. If you are not, you will need to learn large-pot cooking, and the bottom won't be a major constraint. So just pick a pot and use it.