I'll just chime in I guess. lol I can pretty much just confirm that you have been given the proper advice.. A separate tank to treat all the fish and leave fallow for minimum 6-8 weeks. It's horrible, I know, seems like forever but it's really the only way to be sure it is out of the tank. You jump the gun and you risk going through this all over again. Some say there is ich in every tank, me, I don't think so. I have never had it and have gone through like 20 tanks at least in the last five years. I have quarantined here and there, mostly when introducing the older tangs I have from a few years ago.
This is only my opinion, and I am sure some will disagree, but I think a 1.5 inch fish, even a tang, will be ok for MAX 6 months in your size tank. I have noticed that after the first 6 months they grow like weeds, but for the first few they dont seem to grow as quick. just my experience. lol BUT now, that tang is going into an even smaller tank for about 2 months, so you are quickly running out of time to upgrade or rehome.
I would never suggest that anyone get a tang like you have and have no intention on upgrading, but on the other hand, I would also urge anyone who wants tangs to have the proper size tank before they buy the fish. Life happens, money runs out and that upgrade just doesnt seem to ever happen. Just my two cents.
But good luck, you have the advice you need to beat this so you should do fine.