I'd have to agree, you'll be hard pressed to find any table service in your price range. That's about what you'd spend on a typical counter service meal.
Be sure to check out the counter service menus, there are plenty of non-burger options. You'll find the most interesting CS food in Epcot, both in the World Showcase and Seasons in The Land pavilion. AK also has some interesting choices; I especially like Flame Tree BBQ.
Going offsite is certainly an option, but do think about what it will cost you in time. Your time has a value at WDW, considering how much tickets cost. By the time you leave MK, take the monorail or ferry to TTC, take the tram back to your car, drive offsite and find a restaurant, and get seated.....from MK to the restaurants in the Crossroads shopping center, which is probably the closest offsite place for table service....that could be about an hour. Before you even order your food.