I can't believe it's this simple. If anyone else stumbles upon this because they have issues with a jittery/stuttery/inconsistent mouse, all you have to do is install a tool called:
libstrangle
This tool allows you to limit your FPS in Lutris under the "system options" tab.
The problem I described in my last comment is caused by the game's internal FPS limiter. You want to always stay under 200 FPS because that is the hardcoded FPS cap in T6 servers.
In Lutris, set your FPS Limit to something between your monitor's refresh rate and 200. My refresh rate is 170 so I set the FPS Limit to 180. If you have a monitor with a refresh rate higher than 200, you may have to make a bash script that sets it to 180 when the game is launched and then limit the fps to 190.
In game, make sure to disable "sync all frames" and set the fps cap to "unlimited".
Everything runs amazingly well after doing this. Indistinguishable from Windows.