We try to avoid eating at the Studios if at all possible. It's a great day to try fasting (as long as you drink a lot of water!) Bad food at Sci-Fi (I couldn't eat mine, and it wasn't cheap); Mama Melrose horrendous service, ice-cold entrees; Hollywood & Vine buffet not as horrible but akin to hospital cafeteria food. Pizza over by the Fantasmic! line actually made me sick for two days.
As for Epcot, we have ALWAYS gotten into Biergarten, even walking up at 1:00 during Free Dining. Have you tried that one? I've been finding availability all over the place and my trip is in 6 weeks. (Are you trying "lunch" or putting in a specific time? You'll get a lot more options if you put in 1:00 or 6:00 or whatever. Don't know why but it's true.)
For both parks, you could try the restaurants at the Boardwalk-area resorts. You can walk or take a boat there from either Epcot or HS so it's convenient.