Disclaimer: this is not a serious proposal. At best, it’s a thought experiment, but only if you don’t think too much about it.
Florida is interesting in that they are just one of three states (according to Justin Levitt) that explicitly allow for “floterial” districts. A floterial district is one that overlaps one or more other districts in a map. A formerly common example of this type of district arose when a state gained a member of the House, but failed to pass a new congressional map; the new member would be elected by the entire state, at large. These fell out of use with the 1960s reapportionment revolution (though are still the federal statutory remedy should a state fail to pass a map while gaining a seat), when redistricting became mandatory after every census. The only current usage of floterials I’m aware of is in the New Hampshire State House – they place a high value in not splitting towns, and in complying with equal population requirements, they make up population deviations by drawing floterial districts over adjacent underpopulated districts.
But floterial districts could be an interesting way of combating gerrymandering, by allowing both parties to gerrymander. What would happen if you allowed Republicans and Democrats to each draw their own statewide map with half the districts required, and overlaid them into a single, full district plan? Would the net result end up being relatively fair? In the spirit of the re-redistricting of the Florida congressional map that’s going on now, I gave it a shot with Florida’s 27 districts, with a 13-district Democratic gerrymander, a 13-district Republican gerrymander, and a statewide at-large district.