Leaking ducts can either be an easy fix or a nearly impossible one, depending on the type of ductwork and how it is installed. Metal ductwork itself lasts nearly forever, and if it is installed in a basement or attic it is easy to seal. All types of "slinky duct" (flexible plastic duct with a coiled wire inside) is subject to getting crushed/pinched/kinked over time, to coming apart at connections, and will always have greater resistance to flow (so, require more power from the fan, possibly reduced output after long runs) than a smooth duct. It can work okay, but the design and installation has to be right.
If you really only use heat 7 days per year, I would go with heat strips (resistance heat) rather than a heat pump. Yes, resistance heat will cost a lot more to run, but the equipment will cost less and will be less complex (so, hopefully, more reliable).
Mini-split: Lots more motors, controllers, sensors to give trouble, and the equipment price up front is higher. They are a good retrofit solution for a home that doesn't have ducts, or if one really needs the ability to have many zones that are each controlled by an independent thermostat.
Florida is tough on air conditioning equipment, it just wears out. If I lived there, I would want to be able to service and replace the machinery easily and at low cost, because it is probably going to be happening every 8-10 years. I wouldn't buy a mini-split in FL for that reason (unless I had a special need--no existing ducts, etc)
Also be aware that our government recently signed us up to another worldwide protocol that will result in another change in the refrigerant used in our home air conditioners. The change will probably come in a few years. The last time this happened (from R-22 to R-410) there were a lot of technical issues as companies learned what types of hardware/seals etc were really compatible with the new refrigerant. R-410 is well understood now, so if you buy equipment today, there shouldn't be any unknown bugs. OTOH, they will be phasing out R410, so getting replacement refrigerant when you need it down the road could get very expensive (as it is now for R22), whereas the newer refrigerant should be readily available.