gyhcat - kit wines are quite straightford to make so it's best to not make things too complicated. These kits are all prebalanced and shouldn't really need any testing. Make the kits as per instructions and the only difference will be whether you bottle after clearing or bulk age in the carboy for awhile. If you bottle right away, add the additional kmeta at that time. If you bulk age for a while, add the additional kmeta when you bottle. Kit wines don't throw much sediment during bulk aging, assuming it cleared properly earlier, so you don't really have to rack during bulk aging. If you bulk age more than,say 6 months, then you may want to add a little more.
I have no experience with hot weather winemaking like in Florida, and your idea of off site storage for your carboy may work but I would not personally want to do that. I would be more inclined to let the wine sit in the carboy at home for an extra few weeks and then bottle it. You can then let your wine age in the bottles; you could put the cases of wine in the rental cooler if you wish. They would be much safer to leave there than a carboy of wine.
Either way, yes, you need to top up the carboy as soon as it is stabilized.