We have a large family, too. Since you are on the dining plan, my suggestion would be to eat at buffets for your TS's. For some reason, our meals dragged on for HOURS when we ate at a sit-down restaurant that wasn't a buffet. The kids were falling asleep at the table. Our oldest left to do some shopping, and came back about 45 minutes later and we were still there waiting for dessert. At the restaurant in England, after over 2 hours, we finally just told our waiter to forget our dessert and give us the bill. Anyway, I would suggest eating at Biergarten and Teppyanki for dinners at Epcot.
Also, if the older kids split up and go off on their own, just make sure they know how to take the buses back to the resort. And, if they stay at a park until closing, keep in mind that it's going to take a long time for them to get back to the resort. So, don't freak out is they're not back right after the park closes. My teens went off on their own to a park and stayed until closing and they didn't get back until about 2 hours after the park closed. They did some shopping (some shops stay open a bit later), then it took them awhile to wait for the bus because the lines were very crowded at the bus stops.
HTH