I don't know the answer to the question legally--because generally reciprocity is full between all states, so if you are legal in Washington, then in Fl. However, I do know that in some of the Canadian provinces that you have to follow that Province law.
Your chance of being stopped and brake inspection is low, but I have heard of FHP,stopping boat trailers, inspect, weight with portable scale, and ticket in not in compliance. This happened near Pensacola, just before a large tournament two years ago. There were over 50 boats stopped and inspected. I have never had this happen to me.
I did stop on the side of the highway, with my Caracal, and was removing the motor cover because it was chafing on the paint of the cowling. A highway patrol officer stopped behind me with his emergency lights on, and asked if I was having any problems. I told him why I stopped, He walked around the rig, and came back--"good to go". That boat/trailer is under 3000 lbs (scale weight--and I carry the weight ticket with me) single axle, and no brakes, but I tow it with the RV (Air Brakes) or the Yukon XL,
I would say that your chance of being stopped in the Keys is far greater. They seem to be particularly sensitive to oversized or weight loads there.