Florida Plates; How to Prove We haven't Been There Lately.

No matter how much some of the Governors want to, they are not going to be able to demand your "papers" Nazi style.
You may get asked at some point if an area is having real problems, but I wouldn't let it stop me from going. In each case simply stating where you are going and that you're a turtle (carrying your house on your back) and therefore are social distancing should end any questions as long as you don't leave the US.