I ended up reinstalling Windows (specifically I went from a 5+ year old Windows 10 install to a fresh install of Atlas OS [for Windows 11 Pro]) because I was having some other computer issues but that also fixed this problem. Mouse is working fine in H2M with DPI set to 1600 and polling rate at 500.
Annoying that I still don't know what the exact issue was but at least I've fixed it now!