Quarantine not being an option will likely lead to the loss of the Kole tang. He'll be lots easier to net up that way.
The efficacy of garlic as an antiparasitic (possibly excepting internals) is completely unproven. It does have antibacterial qualities, to be sure, but it usually won't affect the Cryptocaryons irritans parasite much. The cleaner shrimp, in my opinion, will be too little too late, especially if the tang is as small as I think he is.
I believe you will unduly stress your corals by raising the tank temperature. The only thing you will accomplish by doing this is speeding up the life cycle of C. irritans. That means more stress to your fish, for sure, and very well could lead to coral bleaching. We raise tank temps in a fallow tank (tank sans all vertebrate life) so we don't have to leave it fallow for as long otherwise. Raising the temp in a tank with fish is completely backwards.
At this point, because you insist on no quarantine, the ONLY hope for your fish is if you give him THE best water quality you can, which can only be accomplished if you're using good quality test kits. I doubt the quality of the Hagen test kit--get SeaChem, Salifert, or better yet, LaMotte (one of THE best the hobbyist can buy). Only then can you be positive that your test results are good. The next best thing you can do is give him the best nutrition you possibly can. This is where garlic might come in, but fishes in the oceans lead quite healthy lives without it, I believe in sticking to what they would find in their natural settings--seaweeds, small shrimps, algaes, and so on.