I'd really like to recommend "Beyond the war on invasive species" by Tao Orion:
https://www.chelseagreen.com/product/beyond-the-war-on-invasive-species/

I think it'll change your perspective on the situation and at the very least you'll stop looking at kudzu as a "pest", "invader" or something bent on destroying a patch of forest.

It certainly changed my worldview... Not that I think you should leave it, no, of course not. But sometimes just changing the way we view things can suggest different paths and outcomes. Currently, your forest certainly needs a small heard of goats, to define a permaculture solution!