Just hang the placard as you would at home.
No problems with out of state (we come from Minnesota). If you have a placard or license plate that is valid for handicapped parking in your home state, it is recognized in Florida.
Which lots are easier more acessible than others?
MK is the least accessible because you still have to take the monorail or boat to get to MK. The bus drops you off in the same area as the monorail and boats drop you off. So, by taking the bus, you skip the monorail or boat portion of the trip.
For the other lots, a lot depends on when you get there and how far into the lot you have to park. If you are at the far end of the lot, you will have a much farther walk than you would have by parking in the regular lot and taking the tram.
The Studio has a lot the is just behind (so just a little farther than) the area where buses and trams drop people off. That lot is not that large though and sometimes fill up, so we have sometimes had to drop off DD and someone else to stay with her while DH parked in the regular lot.
Epcot's lot is very close to the tram area and is a shorter walk than taking the bus.
The farthest part of the AK handicapped lot is pretty far out, but the walk is about the same (although in different direction) than the bus. The trams let you off closer.