Your second residency application would be hampered by the fact that you would have used your government allotted GME funding on the first residency, which means your new program has to come up with part of the funds supporting your salary, benefits & insurance by themselves. If you're a superstar applicant then this might not hamper you, but otherwise it would be a great reason for programs to take a pass.
I agree with others-- if this is truly your interest, practicing both musculoskeletal medicine and primary care, you might best be served by FM + sports med. You really could continue to see general patients as well as your 'specialty' interest patients, and you learn to perform injections, pain procedures, etc.