However, I am looking for ways to remedy this problem. I’m curious about buying 4K downloads of the prequels (or 1080p, at least)
I recommend you use Schormann’s preservation of TPM as a base for your edit. It’s in 1080p, it’s equivalent to the DVDs changes-wise, and looks way better than either the 2011 HD Blu Ray or the 2020 4K Blu Ray.