Don't worry about restocking the coral in tank. Much of the coral stock in my tank was given to me and I can easily fragment some to help start a new tank. You'll find most people who have been at this hobby more than a couple of years will help out. Just PM the people (like myself) who have volunteered when you are ready and you'll get a loadout.
Using calcium hydroxide (slack lime or kalkwasser) or calcium oxide (lime or "superkalk") is a good and reasonably inexpensive way to provide balanced buffering of carbonate and calcium for your tank. You just misunderstood the application. Addition of a saturated solution of limewater (kalkwasser), and even worse lime solids, places a high demand on the system to take up CO2 from the atmosphere. If the gas exchange in your system cannot keep up the pH will begin to climb. In an "overdose", the the pH spikes sharply up, fast enough or high enough to start killing the tank.
Since several hours have elapsed since the overdose, its likely that the pH of the tank has come back down to non-lethal levels. Doing water changes now and in the near future will help with the organics released by the die-off. Frequent changes of small amounts of activated carbon ( 3-6 tbls per 50G tank volume is my ratio) will also help.
Another effect of this accident may be to make your powerheads or pumps prone to seize due to rapid precipitation of calcium carbonate onto the impellers. This can be seen as a hard deposit if you take the pumps apart. Running these pumps in a bucket of plain white vinegar (available by the gallon at the grocer) is a safe way to remove these deposits.
Anyway, you've made the material investment in the hardware, and you still have that. Restocking the coral or re-seeding a sandbed (if you use one) should not be a problem with what has been volunteered. There may the expense of restocking some rock for new seed, dependant on just how hard you spiked the tank. Just keep your circulation up, do those water changes, use some carbon and give it a few days. You may change your mind about shutting it down. I'm sorry for your difficulty and hope its not as bad as it seemed. Good luck.