The picture wth the hairy almost purple-color algae above was from my tank. I now have no algae whatsoever to speak of in my main tank (220 gal). Three tangs, a lawnmower blenny and two turbos plus a growing number of small snails of some sort keep it totally in check. FWIW, I have observed the lawnmower blenny eating the hairy red-purple stuff. I have also observed the turbos. I avoided the mexican variety since my tank temp is 80-82 and they are cooler water animals.
Have you guys considered what would happen when your 50-70 snails begin to die-off from starvation? They are big animals and pollute quite a bit when they die.
Now this said, I do still have the red stuff in my overflow - where light gets to it but no snails/fish, and some in my fuge. Somehow it manages to grow on my Caulerpa. No biggie - I pull it out when I prune back the Caulerpa.
FWIW, I have not found a limiting nutrient for this algae. I have reached nitrate-limited and phosphate-limited lack-of-growth for my caulerpa and have to balance heavy feeding of the tank to generate enough nitrates/phosphates to keep the caulerpa growing. The fish don't seem to mind

. With my current feeding regime, I rely in the DSB and caulerpa to control nitrates and I run a small fluidized bed filter filled with ROWAphos to control phosphate. I have found that removing too much phosphate causes the caulerpa to go sexual, while not removing enough allows cyano to bloom. I run a skimmer but don't heavily skim.
I'm at a happy place now.