thats exactly the kind of tank I like to have in here for examples.
promise you wont leave us hanging on the follow up pics like my other bros from pages gone

yours will look so nice, like a new tank. You can either repeat as needed, or find a new preventative to prevent this regrowth or at least slow it where you use a combo of peroxide and X as needed to maintain perfection from primary producer infestation.
make sure to use a new, unopened bottle.
nearly all the applications on target except for the acan can be done without polyp contact.
no sensitive corals, good detail pics, and a near absolutely great outcome in the works. That acan you can expect to remain stressed for a while, that algae overgrowth is as irritating if not moreso than the little peroxide you are going to get on it because the encroachment is really marked.
But its not a sensitive species...so, even if the tissue acts all wierd, in a few days when the algae is dead the unobstructed tissue will rebound and what you will see is a little bit of the septa protruding out the side of the coral and in time that will regrow. Feed this bad boy directly to speed it up, a little blenderized mysis right in each polyp each morning for three months is the doctors scrip

or just let it go au naturale in the tank feeding indirectly off various sources and it will still be fine it w just take longer to cover up those septa w overgrowth.
I have a frogspawn thats showing septa as we speak from red mushroom encroachment just like your acan. after I zap them with a custom majano wand, it will take three mos to heal, then they will come back and encroach again and we'll repeat the diddy. thats the dance I have to do for success since my tank is so small and so old and someone talked me into trying the evil beasts that are red corallimorphs lol.
Your tank:
I noticed you have a large grain substrate, this is why detail fts help a lot. You know thats catching a little more detritus than normal and factoring into the algae issue but its really not a big deal if you can work a little better during water changes to keep it clean, maybe with a standard gravel vac if that works on that grain size correctly.
thats a lot of water to drain out to access the target spots so it seems you might be lifting out the rock to do external work, good. this allows you to clean up under that structure where currents will have certainly deposited a little mulm. a tank drain is also an option if you have that much water...a big change is fine any time if you match params well. either way is fine.
so as you set that rock out on a towel, no rush, those corals and the bacteria can be emersed for far longer than you feel ok doing it, so maybe keep the total out job to 5 mins or so and you are well within the safety zones. My tank stays drained 20 mins sometimes with 16 varieties of coral just like that

its tuned for a beating quite well.
that live rock does not have benthic growth that will cause ammonia spikes upon reentry, bet on that. unless you use api test kits then be prepared to be freaked out on a .25 reading lol
dropper/paintbrush/dribble on peroxide on the bad spots, let sit a couple mins, rinse off and put back in tank. dont hand remove it, makes for good pics. the minor dieoff of the algae is hardly anything in terms of nutrient stores, a single day's feeding is 10x worse P and N
the back wall can either be scraped clean or with a drain and treat, you can lay a wet paper towel with peroxide temporarily across any patches and let it cook for a sec then lift off.