The game installs and loads fine, but for some reason the cursor doesn't move the way a mouse cursor is supposed to. It feels like it's trying to apply some kind of momentum like it's an old trackpoint or something. I thought this might be fixable by running the game in windowed mode but I can't get that to work, either (it's convinced that my resolution is less than required even if I have the virtual desktop set to 1920x1080).

Old post, but maybe the guy is still looking for a solution...
RRT2 is compatible with a tool called DxWnd, it's a DirectX wrapper (translator) for newer devices to run the game properly. There are a ton of controls there, framerate control, play on window, keep aspect ratio, mouse fixes, CPU limiting, etc etc
Just create a profile for the game, point to the executable and click "Run Hooked" for the hook to take effect.

This wrapper also might help you. It was designed specially for RRT2.
https://verokster.blogspot.com/2019/10/railroad-tycoon-ii-gl-wrapper-patch.html
Follow instructions how to apply it under wine