Hey Ernie,
Well, I had lived in Florida for many years before coming to southern Japan, and both places are suitable for growing orchids outside, even epiphytic ones. My suggestions for epiphytes would include:
Dendrobium, moniliforme, nobile, loddgesii, kingianum, and any of their hybrids. Most of the deciduous caning species should be OK as well if sited well.
Neofinetia falcata and most of its hybrids
Sedirea japonica
Gastrochilus japonicus
Cymbidiums - especially the Jenosa section and honestly any of the large hybrids if grown in slightly elevated beds of pumice and the like.
Leptotes unicolor, bicolor
Pleurothalis sonderana
Neolauchea pulchella
Isabela virginalis
Sophronitis acuensis
Maxillaria varibilis
Coelogyne cristata
Vanda coerulea
Encyclia tampensis and its hybrids
Cyrtopodium punctatum, and any others from the grasslands of Brazil would be worth a shot (if you can find them!)
Harrisella porrecta - these may even be found near you in orange groves. The hard part is finding them - they are tiny.
Epidendrum magnoliae - worth a try, but getting one to establish is another thing. They are surprisingly difficult to get going.
The trick is to find species that can withstand the heat of Florida's summer and not melt in the occasional frost. If you can keep crystalline frost from forming on their leaves, then you can try even more things. The only problem is that below 25-27 F damage will start happening fast with many. Winter deciduous species and terete leaf species hold more promise. Virtually any of the native ones in mainland Japan could have a shot, but most of those are pretty tiny and would be hard to source in the US.
Terrestrials are a pain in the bupkis. Bletilla striata and Spathoglottis plicata are usually no brainers. If you can find Phaius flavus (AKA P. minor), you'll find it to be one of the more cold tolerant species. Of the Calanthe, I would try the deciduous bulb forming ones from SE Asia. Japan's species except those of the southern islands (sylvatica, triplicata) are too temperate for your climate I think. If you can source some, the south Florida native Bletia purpurata may do well in a sandy bed. Bog species that are pretty easy include Calopogon tuberosus and Plantenthera species native to the southeast.
Beyond that, I highly recommend trying some epiphytic ferns, especially Platycerium bifurcatum (very easy and cold hardy even here) as well as P. superbum (stunning, a bit less cold resistant, but still a good bet for you). I'd also get a hold of Asplenium antiquum, the most cold hardy of the large growing birdnest ferns. The hard part will be finding true A. antiquum since most plants on the market are A. australasicum. Another great genus is Pyrrosia with lingua being the most common, though you can no doubt source hastata if you search for it. If you can get hold of the green penny fern, Lemmaphyllum microphyllum, it too is a great little epiphyte. All of the above mentioned plants are cold hardy down to 27 C and even lower if the freeze is not long in duration.
Don't even get me started on tree ferns...