For the future: In general, you never want to cook anything with rice. You approach turkey rice soup as 1. Making rice from beginning to end (however much rice you think you'll need) by itself. 2. Making the soup broth with the meat, vegetables and spices. After each is finished cooking, you then bring them together just as you are serving. Do not mix the rice in with the soup on the stove. It's mixed together with the soup in the individual serving bowl. And when you refrigerate the leftovers, they go into the fridge in individual containers in order to keep the rice at it's best consistency. If it stays in the soup, it turns to mush.
I don't know that there is much that can be done to save your dinner.
Mushy rice... burnt rice... uncooked rice... all mixed with everything else... in my opnion, it's pretty much of a total loss. Maybe someone else has an idea, but all I can do is help you not let it happen again.
"Food is our common ground, a universal experience." - James Beard