Okay, all of the timing and slow down issues are related to windowed mode. If I enter windowed mode it starts the slow down and that persists until I change back into fullscreen and then it persists between restarts until I change the resolution.
I see! That makes (some) sense, as 3D accelerated windowed mode is notoriously problematic. I'm guess it is indeed one of those cases of the driver not synchronizing every frame, but I'm not quite sure what to do about it, as that's something that's supposed to Just Work(TM) with SDL. (I'm not using OpenGL/Direct3D directly in this game, so I don't have direct access to the full APIs.)
I'll see if I can make a build with the latest versions one of these days, so we can see if that has any effect on it.
Well, I've seen a number of ATI/AMD specific issues through the years, and even did the occasional hack to get applications to work with them, so it's not all that far off to assume they're at fault yet again. ;-)
Not much I actually can do through the SDL API, as it wraps these details - but I wouldn't be surprised if there are workarounds in newer versions of the library. You might want to try replacing the SDL.DLL that comes with the game with the latest one (2.0.12, 32 bit) from here:
https://www.libsdl.org/download-2.0.php