couldn't see that pic above till I refreshed, that gives good detail. Something we can work with for sure
I don't play kid gloves with reefs, I force them to do my beckoning so contrast my advice with others that w build in this thread so you have a choice
if your tank was mine this is exactly what I would do and it would work 100% for sure. you may not like the fish part, but its what id do:
the tang albeit debatable for this tank isn't timed right. that's a luxury addition if ever for this tank, only when corals are growing and the major ecosystem is behaving. he's causing you to have to be careful on how you fix this ecosystem, so he's bad for that reason alone. you cant be as deliberate with him, so, id give it back or house it at the LFS until conditions allow.
I would place all coral frags, live rock, and fish in holding buckets carefully netted and lifted out. This will leave now only a tank with *undisturbed* sand bed cuz you haven't done anything yet to it, and water, and the growths on the walls of the tank. the rest is sitting in home depot buckets.
You dump out all the sand and not reuse any of it. not rinse and reuse, dump it out and start over w new sand for specific reasons of phosphate binding in the current condition. So the sand has now been dumped out, leaving only an empty tank with growths on the walls.
scrub every surface of the tank clean w vinegar and a razor blade to not scratch.
put in the highly rinsed caribsea sand, pre rinsed so well that when you pick up some and drop it underwater, no cloud forms. rinsed well. its bacteria are incidental and not needed now.
summary
you now have a crystal clear tank with pristine white sand or pink or black, clean brand new saltwater made with a 100% change. that's all that's in the tank.
reacclimate the fish from the buckets back into the tank without the tang.
now in the buckets is just the rocks and coral frags
clean off any areas of growth on those rocks with a toothbrush and a scrubbing of peroxide to get off the algae and growths, rinse that off and start stacking the rocks back in the perfectly cleaned tank that has 100% new saltwater from any brand.
clean each frag plug off *at the base* with peroxide so that you are reimporting as little algae as possible.
don't get it on the corals, this is for hard substrates to help remove algae and import less into your new tank.
So the new tank now has 100% water change, all new sand, totally clean corals and all rock surfaces its brand new now and doesn't have to recycle.
You need to focus on having hardly any fish at all, as their major waste contributed to your algae issues. focus on changing large amounts of your water weekly for two mos as you spot feed the corals with hq frozen feeds, then in a few mos when things are better consider reupping on fish. if you do, expect another cleanout next year, that's a high fish bioload currently.