Been there and done that...... not fun. Still have a couple of 5 gallon buckets of coral skeletons that I'm too sad to dump. A gallon of Randy's 2 part Alk solution in a 120 is kinda nasty.
Brett is right try multiple small water changes until the Alk is back to normal ranges..... sudden changes are discouraged. Also, try using a turkey baster to keep the precipitate off the corals, maybe even siphoning through a filter sock into the sump. Also, if you have a sand bed make sure it does cement up, if I remember right it's worse in a deeper sand bed. Just clean it like you usually do. I wish you good luck and keep us posted.