Considering that these runs are for Toontown Rewritten (with the rules specifically forbidding other servers, presumably including Toontown Online), should the box art be changed to match this? A suitable replacement would be the initial title screen ().
IMO if it's a toon using a Unite on theirself, I don't see why the run can't stay solo, though I can't really speak since I'm not really in the speedrunning community for this game.
I agree that Toontown Offline runs should be a separate game/"platform" due to the fact that Toontown Rewritten may change tasks that Toontown Offline does not, along with potential speed differences in the versions of the engine used and other factors. Of course, we'd have to deal with how to handle Toons that are in states that are impossible to achieve in TTR (like having all 7 gag tracks).