Thanks cstanick! I did a little more research, and I found another workaround that seems to do the trick. If I run the game outside of Steam by opening the app itself from the local file, as opposed to running it in Steam, the mouse lag goes away completely. This worked for someone back in 2019 (right after I took a break from the game) and its definitely working for me. Even though I've turned off the Steam overlay and set my language to English, the issue still happens within Steam, so it seems to be a Steam-specific issue.
Just happy I can play the game again!