Green windowed borderless 4k mouse offset issues

[GoldRidley]

The problem: I use a 4K monitor, but to prevent my eyes from exploding, I want to play the game at a lower resolution. I also want to be able to alt-tab and interact with the rest of my desktop without windows crapping itself.
The only known solution: a borderless fullscreen program to stretch the client across my full display area.

I've tried all of them (yes, even the thing you're about to suggest) and they all have the same problem: the visible position of the mouse cursor is way out of alignment with what the client recognizes; i.e. I click at the center of my screen and it registers the click at the bottom right.

Because green forbids custom UIs, I can't simply install one of the excellent community-made 4K UIs, which would let me borderless fullscreen without scaling/stretching, which works fine.

What do? Thanks.