Thank you all for the good advice. You may be right about adding the fish too fast... I'm just so use to fresh water... I could add five at a time, do daily water changed for a week or two to keep ammonia down, and everyone would be perfectly fine without the slightest problem.
Just as an update... of the two clowns I got, one died this morning. When I was pulling him out, I noticed the second one was breathing faster. I snatched him up and put him in a QT tank and put some melafix in... I didn't know what else to do and that treats a whole host of different things, so I figured it couldn't hurt the situation. He's not looking any worse now, but he isn't looking any better either.
Innovator sent me a PM with a pretty good suggestion that I think I'm going to try... He suggested taking a spare tank (a cheap 10 gal
petco kit I got several months back in my case), thoroughly cleaning it out (obviously without soap or any of that), and putting RO
/DO water mixed with salt and set to the same pH as my main tank. Use the raw shrimp method to get the cycle going, then take a couple blue damsels and put them in to see what happens. If nothing goes awry in a week, then take some live rock from the main tank and put it in. If all goes well, then maybe some sand from the main tank and basically keep going until the fish start looking unhappy and then I have found the culprit.
At this point... that really seems like the only plausible way to solve this thing.