I eat solo pretty often at WDW since my travel companion is often done in at that point. I don't go anywhere where there's a group table (I gather Biergarten is like that) and I'm not usually into character meals but I love Tusker House, so I always have a meal there every trip, either with my travel companion (my sister) or by myself.
OP, you should just go to the TS restaurants that you like and avoid the places with group seating. I don't know where all those places are, but perhaps someone else will chime in and let you know. You might want to avoid '50s Prime Time, since there's interaction with the waitstaff, but you wouldn't be seated with anyone else at your table, if that's your main concern. You'd probably be seated with a group at Hoop De Doo as well, but that's another animal altogether.
And enjoy those single-rider lines! The one for RotR is always quite short.