New corals wouldn't / shouldn't cause amonia spikes, unless there's critters on the corals that died. I would retest ammonia to make sure it's not a false positive.
For Alk, what test kit are you using? I'd compare with another test. You don't want to fix things that aren't broken. If things are not dying (as they should be at 16dkh) I wouldn't fix it, I would retest with different test kits. Test your water change water as well. What alk does it test at? Hopefully at this point a couple days, if the tank is cycled and went through a mini cycle, it could be over already. If fish and corals are behaving and not showing signs of stress, I wouldn't do too anything too invasive other than more tests. Don't overreact. If test numbers are wrong then, reacting to false information creates new problems.