the reason peroxide is so worth trying on this is because all your coral is tolerant to it, applied specifically in a controlled manner. if the target happens to respond you have cure gold in the making
you would drain the tank down and expose the target areas and spot apply it. those corals can be out of water 20 mins easy and we'd consider something like a 2-5 min drain and treat, but only after a test rock. im feasting on those pics contemplating what an after shot would look like. peroxide is a common metabolic byproduct of photosynthesizing organisms on the reef so tunicates that may be strictly heterotrophic might not have the complement to deal with some peroxide. we know from countless other threads how to apply it in your tank without harm, if the test work. if a single test rock taken out, treated and rinsed doesnt have mass dieoff in 5 days Id strictly consider animal grazing as your best option.
I wouldnt do a tank takedown, you are unlikely to get this out of any part of the system that would be reused for the new tank, including fish slime coat layers. There are macro, ultra high res pics online that show standard reef fish with invasive dinos stuck right to the side of their slime coats, taken from an expensive pro model dslr cam
its from the chem forum at rc, dinoflagellates thread. the whole point of his post was how in the world did dinoflagellates get from the infected reef into the new, I sterilized all the rocks?
to me, its simply not worth the money to start over, lets test the clearly obvious cheap options first and hope for a lucky run. if peroxide works on a test rock, it w fix your tank for .75

but its a surgery for sure to get at that intertwined growth. we did equal surgeries in the various perox threads online.