From my own experience, and, I had the hair and then the bryopsis infestations from H@!!, none of the animals-fish, urchins, sea slugs, ect- will cure the problem. I tried all of them, including a foxface, several lawnmower blennies, lettus sea slugs, urchins, snails, hermits, ect. Yes, most of these critters will eat the algae, but, most will not touch the long stuff, and none of them, even several types together could make an appreciable dent in the growth of the algae. They all seem to prefer any other food to the algae and soon stop eating it, anyway, so whatever effectiveness they may have had ended as soon as they 'discovered' other food sources.
What finally seemed to work for me, was a combination (IMO) of upgrading to a better skimmer, constant hand plucking, and, reduced water changes (I use tap and it is bad). Also, I think many of the algal outbreaks tend to be somewhat self-limiting and start to die back after a certain length of time, anyway. I fought the algae for over a year and then it just started to die out. I still have a few small patches that I still hand pluck, but, they don't seem to grow back like they used to. Getting nitrate and phosphate under control is certainly a priority in getting an algea bloom under control. If you don't, all the 'algae-eating critters in the ocean are not going to cure the problem, they will only add to it. HTH