I disagree that that is a Rhodactis spp. mushroom. The only Rhodactis mushrooms in the Caribbean are the Warty Corallimorphs which are distinctly different; much larger, have larger vesicle "warts", and will curl inward when disturbed. Their tissue is also much more "jelly-like" and watery. If you want to see a "true" red Rhodactis from Florida, check out my recent post of my 18 gallon caribbean corallimorph tank. You will see 3 types of Rhodactis sanctothomae morphs; blue, green, and red. I have only seen 3 of the true red rhodactis in all my collecting.
What you have there is most likely a red morph of Discosoma carlgreni, or perhaps an undescribed species of Discosoma. The red color morph is not described in Paul Human and Ned DeLoach's book on Caribbean Reef Invertabrates. These red mushrooms are found in the same habitat as both the Discosomas and Rhodactis, and are fairly uncommon, although not rare. I saw 2 of these on eBay go for over $100 not too long ago, and listed as Rhodactis sanctothomae. I would say that that is an incredibly inflated price for these guys. When we go out and collect we might get 100 or so in an afternoon (of course we are going to very specific locations where we know them to be plentiful). The real rare red morph of this species are the ones with the bright fluorescent green mouths. Maybe about 5% of all the reds have this. You can see some pictures of these on the same post that I mentioned above. I also have one up on eBay right now along with 7 other really rare Discosoma morphs from the Caribbean sold by "Caribbean_Corallimorph".
Anyway, I think it is about time that we set it straight that these reds are NOT Rhodactis, but I would agree that they do need a scientific taxonomic classification, because I don't think that it has been done yet...