I am not an insurance expert but as far as I know Traditional Medicare with a Medigap policy that allows you to self-refer to any doctor/clinic accepting Medicare gives you choice. Also, since you live in Florida and are considering going out of State to Rochester, Minnesota, the Medigap policy should allow you to travel. Insurance choices are also based on residence so you can check the Medicare site to see which plans are available to you. Also look for your Part D drug plan with the Medicare tool. It is quite good. You give it all your drug information and it pulls up plans for you and gives you estimate of costs. There is an extraordinary difference in drug plan costs which I do not understand despite asking sales reps about it.
I am a patient of Mayo Rochester for lung cancer (I self-referred) and had no issues with my Traditional Medicare Part A, Part B insurance and Medigap plan. I never saw a bill.