I think as far as swapping out turkey for beef or turkey burgers in the park, you are out of luck.
Here are some alternatives:
Geyser Point has a Bison Burger that gets pretty good reviews. It's not turkey, but bison is a leaner meat than beef, plus it is a short boat ride from MK.
The Fountain at the Dolphin
Beaches and Cream- they used to have turkey burgers as an option, but no longer. That said, if you get a single with no cheese, I think you wouldn't be doing too terribly bad. Plus you can swap out fresh fruit for fries. The burgers themselves are a little bit on the thinner side, versus the big thick burgers; plus, the actual quality is worth the splurge (both health-wise and $$) Of course, good luck getting out of there without getting some ice cream, which might defeat the purpose, but still.
Both the above are an easy jaunt from Epcot or the Studios.
Also, keep an eye on D-Luxe Burger...they sometimes have seasonal special burgers...it may not be turkey, but it might be chicken or chorizo or bison. At one point, they had a pork belly burger.
Lastly, you could order a Kids' Burger. Yes, it would be beef, but the portion size would be a little smaller and maybe more doable. If you are somewhere with a toppings bar, you could load up on some of the healthier toppings and probably have a pretty substantial sandwich.
