I've run into a bunch of issues though, starting with Livesplit not being visible on my screen over Dishonored if its in fullscreen.

People normally have their livesplit open next to the game's window, or on another monitor, then add it over the game in their layout in OBS. I'd recommend doing that. I run the game in a 1600x900 window and have livesplit open next to it (1080p screen)