Palemoon, being built-in to fossapup64, is an easy update, and so I recently updated to version 31, and it seems to have solved the cpu issues that I was experiencing with version 30. I posted in @mikewalsh's Brave-portable thread that I was pretty sour on Palemoon after the recent releases, but I've always appreciated the browser, and so I'm going to be using it again.
I'll report any issues as I find them.
Direct download from here:
https://linux.palemoon.org/