Rootstock has nothing to do with everbearing, that's strictly controlled by the variety that fruits.

key lime cuttings should do ok in a pot but grafted to a dwarf stock would be better.

a key lime is a key lime is a key lime. Grafted, from seed, cuttings, you couldn't tell the fruit apart. The only key lime that's different is the one I have. The giant key lime. Same flavor, bigger fruit.

you live in Florida, I wouldn't move any plants because of hlb, but your state already lost the war so idk.

a heavily pruned tree to keep size and shape will loose most if not all fruiting wood. But I doub you would have to prune that much.

why couldn't you plant in ground after you move?

key lime fruits the fastest from seed, just a few years. Growing from seed is a better option than cuttings that might have diseases.

Ps. I'm not a nice guy. My homeowners association if I had one, if they told me I can't keep the tree, I'd chop it and leave it where it falls. You bought it not them.

-I should have been clear, when we move it will be within the state. I am very aware of hlb having lost a Meyer and a Mandarin to it and wouldn't dream of moving them out of state. My apologies on not being clear on that.
Thank you for the answers though, I will get some cuttings and maybe some seedlings- going in the spring.

PS. I am a nice guy, or at least an honorable one. When we moved here I had no clue I would get caught up in growing plants. There were certain things I agreed to when we moved in and I would not go back on my word simply to spite them.