You aren't going to rank the Florida core site as number 1?
The good news is that I've already (almost) done the having to move from site to site. Let's say you get your 3rd choice and end up at Knoxville. You're there for month 1 and 2, but month 3 is your elective in Florida. Just tell whichever preceptor you are with that you need to leave early on that thursday or friday because you have to move. 100% they will be fine with it. If you have a comat on that friday, you're only there for 2 hours and then you're done. If you know you need to leave that thursay, just speak with the comat dcom staff and ask for the date to be moved because you have to travel cross country. They've already had to move some of my comat dates because of comlex PE.
If you are concerned about packing and traveling. I was able to pack my car in under 5 hours, leave on a friday morning, drive 13 hours, stop at a 24 hour rest stop, sleep for 6, then kept driving for 10 more hours and that was a Saturday afternoon/ early evening. So you'll have some time to make the travel time.
As for living arrangements for that one month, I'm using air B and B to find some places and I think I've seen rotating room being suggested.
You also have one last option, is that after you get your core site and you're given that individuals email address. You can make a compelling request that you want all of you selective and elective rotation grouped together because you want them at one specific (long distance) location and having to travel back and forth is a killer. My core site coordinator worked with me on it, but a new person then became our coordinator and I doubt that person would make the changes. Then you just keep dcom in the loop and it's all good.