OK, I've (finally) managed to get it to run in 3840x2160. Took some doing, figuring out what was wrong, but I got it sorted.
Essentially, on Windows 10, it now has a setting to "override high-DPI settings". This is the future; with higher-resolution monitors rapidly becoming the norm, UI scaling is presumed; applications in pixel scales are definitely going to have various issues. So that setting is mainly for legacy applications that cannot respond to requests to scale things like UI up, applications that won't request large-scale fullscreen, etc. I had to set that to "Scaling performed by Application" to get this working right.
1. It won't run fullscreen. It throws an error. This is odd, since it works in windowed mode. But fine, whatever, it's using the whole screen, right?
2. Interestingly, performance is not impacted greatly. The game's still CPU-bound. The load shifts a bit but not the root causes.
I'll probably take another long look at that, see what's up at this scale, since FWIW, this is where more people than not will be in a year or two (i.e., around Gold). I definitely feel like I should turn Vsync off and see what, if any, impact that has (I can't imagine much, given that the OpenGL state-machine's in lockstep with the game logic, but hey, who knows).
It might also be interesting if we could lock the state-machine to lower speeds but keep the rendering engine higher, take advantage of some frame averaging, etc., rather than just some buffer-swap.
3. It's pretty glorious seeing the battles at that scale, but the full-screen whiteout on ship deaths is definitely *not* a great thing at that point; really should be something that does some gradient and makes use of the scale better. There are few things more unpleasant than getting a face full of bright LED on a modern screen, though.