Are you sure this is hair algae and not a species of Bryopsis? If the latter is the case a CUC will do nothing. I’d pull some out and identify. Bryopsis is very common on Florida rock.
If Hair Algae:
Easiest thing you can do is turn off the lights and manually remove as much as you can. CUC won’t really touch the algae when it’s long and flowy. Keep the lights off once you add the snails/inverts
Your best bet is turbo snails, pitho crabs and urchins. They are the best for eating larger filamentous algae. Trochus/margaritas and astreas are not great at that ime. Yellow tangs are good but bristletooths are more voracious for picking at rock.
If Bryopsis:
Some of the algae you’ve shown looks to be fern like (see below), which is a dead giveaway that it’s Bryopsis. If that is the case your only option is either a full tear down or nuke with fluconazole and turn UP the lights ironically. You then have to hope every last spore got killed (easier in a tank with no coral, since you can run it for much longer)