I understand your concern about dining sit-down solo. I used to be very uncomfortable. But I finally found something that really helped. Before a solo trip, I buy a little spiral notebook, about 50 cents, at a drug store. I carry that notebook and a pen everywhere. I use my resturaunt time to write down notes on what I've done, rides, where I've been, opinions, any future plans. This not only serves to keep me busy, but it's a great little souvenier-after I come back home, I can read it when I need a "Disney fix". And something I didn't plan on, a couple times doing this has gotten me what seems to be better service. It's like the CMs think you're some kind of "undercover" Disney executive, making notes on the resturaunt service, etc.! Didn't think of that!
Just one thing-before I go, I research resturaunts so that I avoid ones where the lighting is too dim to write-for example, Biergarten and Mexico I'd avoid for that reason.