Not sure this is a good idea. What if the disappearance of corals at higher temps is part of a natural regulation system for Earth, where if they are artificially preserved, homeostasis will be perturbed? In general I am against these ecosystem engineering type projects: because the systems are so complex, we do not understand them, and we cannot test in isolation.
Of course there’s no engineered homeostasis to mess up on Earth. There might be a general tendency toward homeostasis: lots of, in some generalized sense “mass” and “momentum” in the system, and a tendency for species to die off by consuming all their resources and running out of places to put their byproducts. But that seems more likely to be something that humans fall afoul of, not coral, which seems more like an accidental victim and evidence that homeostasis has some pretty big gaps.