Laser clear pics and setup, nice tank wow! We know your sand is clean a la goby

so detritus doesn't factor, only unlucky hitchhiking-this plant needs only a ride in to set up shop and a missing grazer to expand after setup, not sure who the right grazer animal would be
I have two thought modes in reefing: how can we get a cloudy tank cleaned and 2. What can be target killed with peroxide
That algae is among top 3 most susceptible to peroxide / helpful character
Large tank= hard to pull and treat rock yes but so far nothing works anyway, we can model some proof and then you choose the upscale if needed
Fluc is a good choice. Not being the result of detritus problems it's a fine thing to try
None of your corals are peroxide sensitive in the known safe dose so as another option we can prove readiness wo experimenting with your whole reef, by two test rocks
Try to access one test rock somehow lifted up and out of the tank
Pour peroxide across target, avoid coral, straight 3%, let sit for a minute or two cooking, rinse w saltwater, leave the algae attached and put back. We chart it's tested dieoff and growback if any. This represents tank access and spot kill, hard work, but easy to model.
Second test models the easy option, full tank dosing. Take another test rock and sit it in a five gal bucket of saltwater with half a milliliter of peroxide in the water
Submerge test rock a few hours/half a day then pull it out and put back
We will know in five days what works for sure, wo risking your tank during testing
This species is top 3 easy to kill w peroxide. Any lysmata cleaner shrimp are a loss risk...weakest animals we keep regarding peroxide use