Have you tried ripping it down? Most CUC won't attack algae that is too 'tall'.
Having said that, it looks like bryopsis to me. Which... you're actually not far off. Very few animals have a taste for bryopsis. Some emerald crabs will touch it, but most won't; I've had at least a half dozen of them over the years, and only one of them has ever eaten it. Most fish aren't interested in it either. In fact I've never heard of a fish that will eat bryopsis.
About the only reliable treatment for it is fluconazole, which is sold under the name Reef Flux. It's usually highly effective within 10-14 days. There are a few other things you can try as well - manual removal coupled with nutrient control is the next most effective, and some people have had success with raising magnesium to 1500+.