I'm in 'chaotic good' territory, with the smaller secondary monitor on the left, and games fucking refuse to launch on the larger monitor despite it being set as the primary. Even doing the Win+Shift+Arrow trick to force it over to the right, it will pop back to the left as soon as I Alt+Tab away, or sometimes even during the transition from the main menu to loading the actual game.
Tried switching the ports around to change which monitor is #1 vs #2; I've even upgraded to a new GPU... nope, shit always launches on the tiny monitor.
Ready to throw them both away and just buy two matching monitors, but y'know... money...
What window manager do you use? Many have an option to overrule what the window wants to do and force it to do what the WM wants it to do. This might solve your problem.
Ah, for some reason I thought this was a Linux sub lol. I am not too familiar with how the graphics stack works on windows tbh nor how to customise it. Sorry.