Holy water?
Seriously, it's a pain in a 65. VERY hard to get rid of. I tried urchins, snails, crabs, a rabbit [never again! ich and bad behavior: it tried to eat my frogspawn and bothered my clam, plus terrorized other fish], young purple tang [but he couldn't get the roots, and terrorized the other fish, not that he ever offered to harm them; and it's not a good size tank for a tang at all]. And I cooked the rock. 2 things survived: one aiptasia, and the caulerpa. I couldn't believe it.
What finally got it: a REALLY big refugium [20 g] with a 20 hr light cycle. AND a kalk reactor. Now, what part either played I'm not sure, but both together got it: I watched the last of it turn pale and die out without my touching it and it has never come back.
In a situation of limited space [I have my sump in the basement: drilled 2 inconspicuous holes through the living room floor and put the whole support rig below] I'd do a temporary closed loop to a well-lit 20-30 g tank/refugium and see if that will do it. If it gets it you can go back to one refugium and relax.
If that doesn't get it, you have to add a killer skimmer and a kalk drip...which is the other part of my successful equation: I upped my skimmer to an Aqua C EV 120, [for a 120 g, on a 54g bowfront] AND I added a kalk reactor driven by my topoff pump. The deal is---kalk causes a tiny amount phosphate to precipitate out, and I set the drip right above the intake for my skimmer. So if what an old reefer told me is so, it's getting a little phosphate skimmed out, too. Bertoni says it's so little as to be negligible: probably he's right. But my caulerpa is gone---you do know that phosphate is what it has to have in order to grow, and the way the refugium works is giving an advantage [in lighting] to the cheato to grow bigtime, taking up all the nutrient. My cheato ball is the size of a basketball. So I mostly credit it.
Don't rely on phosphate removers per se: your tank won't test positive for phosphates as long as you have algae growing: it's 'inside' the algae and won't show on tests. So it can't be uptaken until some algae dies and releases it into the water. Fish poop can do this. No-light can do this: turn the lights out on your display 3 days, then actinic only the 4th [so as not to shock your critters] and back to normal. Do this once a month. This will start inconveniencing the caulerpa in the display, and give any phosphate it releases to the cheato. If you are confident of being able to get him out, finding a small tang that can [temporarily] eat away would be good. BUT you must get rid of him when he's done, or you'll only be feeding more phosphate into your system keeping him fed on nori, so have an understanding with your fish store.
Understand, too: phosphate enters your tank from: non ro/di water, ro/di water with an expired filter or membrane, pellet/dry fishfood, nori, veggie food, etc. If you're going to feed phyto do it down in the fuge where your copepods are.
It's a tough fight.
