Couldn't you have a floating hole filled net to give shade over larger areas? I guess this is the early stages of testing the idea, but if it's promising enough, I think floating surfaces are the way to go.
Unfortunately stony corals also face a grave threat from ocean acidification due to rising CO2 in the atmosphere. They need alkalinity to make their skeletons.
Shading can buy corals time against heat and light stress, but it does nothing about the declining carbonate availability they need to keep building skeleton
Have to nitpick though, umbrellas protect you from falling water, parasols block light.