Great discussion, lots of possibilities, lots of great suggestions....
Let me dissect a few

Clearly all the suggestions are good ones, but not every one could be used in every application... If I shoot down your suggestion, please remember it's only because it isn't practical in THIS application, which is not typical of the applications on this board, but because it's a "remotely operated" tank. Put it this way, they don't spend any time observing the tank, so if a fish dies, they aren't even likely to notice it's missing. I "take attendance" each time I go, and if somebody's AWOL, I ask if they remember the last time they saw it. Sometimes they remember, sometimes they don't. They've only lost a few fish since the tank was established, no serious disease outbreaks or anything, but thank goodness they have a good cleaner upper in the serpent star....he disposes of any bodies. All of the inhabitants are "original", all there over a year they have not replaced the ones that have died. The clown and the serpent they have had for several years, prior to this tank, they had a 30 that was poorly maintained by somebody else, and when I came to their service, the tank was leaking and nitrates were over 160 ppm

. It was a FO there was no LR, no skimmer, it was a nightmare. So ugly or not, this current situation is still much better than say, 18 months ago. But I digress....
Reminder: The tank is a 52 corner FOWLR. It was meant to be a reef (and I'll convince them someday to make it one!) the only corals are some buttons, shrooms and a Xenia frag. I have no leathers to be adversely affected by phosphate sponge.
Seachem Phosguard does not leach junk back into the water, but I replaced the first round after 1 week and I've left the second round in for 2 weeks. I plan to remove it next week, as it's looking exhausted. I use Kent carbon too, no phosphates.
The feeding issue....they aren't starving the tank by any stretch, but I think I've convinced them to cut back to a pinch of flakes (for 4 small fish that's plenty) or a half cube of brine or formula 2 every other day. IMO they could cut back more, but that's what they are doing. The hermits, arrow crab and serpent star should take up any leftovers.
They do have a couple of "grazing" fish, the lawnmower and the flame angel...however they don't graze enough, they like the prepared foods they are given

Not too many species really like hair anyway....Atlantic Blue Tangs do, but they get MASSIVE and to get one in, I'd surely need to have an exit plan, and I don't just now. Perhaps later, as a last resort. They do have Mexican Turbo snails, but probably need a few more, as they've lost a couple in recent months.
The skimmer is rated for a 150 g tank, and it's powered by a Rio 2100. For a 52, I wouldn't say I'm underskimming. I cleaned out the impeller assembly and tweaked the skimmer last Thursday, just to make sure it was firing on all thrusters. It's twice the size of the skimmer I have on my own 37, which I feed heavily. Their skimmer pulls a nice thick brown skimmate, in decent but not abnormal quantities. It's great on toast
DSB......hmmm, I'm not convinced that DSBs are the holy grail of water quality. (I know, I know, but save your arguments because I'm not listening!) My own personal tanks don't have 'em, and I'm not having algae or nitrate issues....I won't rule it out, but honestly, I think they are ****ed unsightly when they get their "geological" layers, and I can tell you my client won't like them. Keep in mind this is not a "hobbyist" tank, but a "for show" tank. They only want it to look pretty, not practical. IMO also a DSB would look very awkward in this tank, just by virtue of its shape. It's a hex with 90 degree corner on the rear two sides
BTW as I mentioned, there is no measurable nitrate in the water with a standard hobbyist grade test kit (I've used 2 brands on this tank) so if there IS a nitrate issue, the algae is dealing with it effectively, if not aesthetically.
The tank DID grow Caulerpa racemosa that hitched in on the LR, I used to prune it, but eventually the Valonia took over, and the racemosa crashed. Not sexual, it just dwindled away. There is also a decent crop of Halimeda spp. in there, I prune that sometimes, but haven't had to lately because the hair was doing most of the growing. The hair choked out the Valonia, so that's one good thing I guess

. I COULD put some C. prolifera in there, or some
feather caulerpa, but then I'd have the overrunning problem of that. Being a corner tank, there's not a lot of room for play. Ditto with the sump, being a corner tank the sump is tall, rather than long, and it's pretty cramped with the large skimmer and the Sen 700, I've got NO room to make a refugium. To the person who suggested growing Xenia or another octocoral weed, there IS Xenia.....it's winning in its little corner of the rock versus the hair, but it's not going crazy. The lighting is 2 x 55 w PC, the Xenia is high up in the tank. I don't know if it's a lighting issue or what, but it's not going nuts. FWIW I've never had Xenia overgrow, but I do have a Coral Beauty that loves to eat the stuff in my 55
I'm inclined to get a hang-on specimen cup, drill holes in it, and hang it in one rear side and put some caulerpa in it, and see if that works. Of all the ideas suggested, that's the most doable for this particular tank. It won't be
reverse photoperiod, but it might help somewhat. At this point it can't hurt too much (knock on wood

) I can always find takers for extra caulerpa so I could start my own little farm in there LOL.
As for Kalk, reactors etc. They aren't going to spend money on a reactor....they don't keep corals (other than the frags mentioned, all soft corals) and they have coralline out the wazoo so I can't tell them it will boost that....I already scrape it off the front glass every time. Kalkwasser...well there's no room for a 5 gallon doser, maybe a half gallon doser, and then I'd have to go there every few days to refill.....I'm not working for free, and they aren't interested in paying to see my face twice a week. Again, if the animals were at risk, that would be another story...but this is really a cosmetic issue at this point, the health of the animals is not at risk. The bristleworms LOVE the hair algae, I had to wear gloves during my scrubbing operation because the hair was literally crawing with them. I threw them back into the tank.
The fact that this isn't mine or another hobbyist's tank makes it a whole other issue. The customer does ZERO maintenance. They just feed, and "top off when the tank starts blowing bubbles"....(I was ROFL at that statement....SO TRUE!). I made a low and high water mark on the sump for them, so they could always make sure that there was enough water, but not too much (in case of power failure, we don't want a sump overflow!), but 90 % of the time, when I show up for maintenance, the water is below the "low" line, but not blowing bubbles yet.

That's another reason why the in-sump refugium idea is a bit less than ideal, because they'd let it dry up!
I'll check on the tank again at the first of the week (another free courtesy call) and see how things are doing, like I said I'm hoping I've turned the corner with this, if we've stopped the overfeeding (and time will tell if they have slowed the food down).
Keep the info and suggestions coming....I think I'll try the in-tank confined caulerpa and see if that helps, but if anybody can think of anything else, I'm open to suggestions.
Jenn