If you already have a Tommy tang, why not "hand" that fish when you add another one or two with your currently healthy fish?
The way I see this, it that your current tank is perfect and the naughty fish needs to adapt. Seriously, why risk adding a new fish when you have a healthy fish in your system? I
would advocate that, if you can, you might wait to find a tang (or 2) that another reefer is rehoming and see if you can find already tank acclimated adoptees so that the fish are tank proven before you dump them in.
This is probably not going to work if you are looking to acquire small tangs. Those you will probably have to purchase, but something to consider.
Disease is another issue. I prefer to pick my own fish from the store. I have more than a few decades of experience that guides these purchases. I cannot recommend that others try this method because fish do die and I do not want to be blamed for that. So yeah, I dump fish and I'm probably a bad person for that?
If a fish isn't healthy enough to "dump" I don't think it will survive in a QT. Please take this opinion for what it is and follow or ignore it at your own risk. Sick fish spread disease to weak fish, so you also need to confidently know the health security of your home tank whenever you are considering adding new fish. I will not buy or dump or adopt even a *free-$5000 price tag fish* if that fish appears to have the plague. My ability or skill level to heal the infirm is not as good as some of the fish husbandry experts who argue for Observation & QT on this site. They can bring fish through. I cannot.
*For the record, I have never been offered a free $5K sick-fish. I might bend my dump rules if that would ever happen? Still, how would I explain this failure to my wife if her tang died as a result of my error in judgement? Good night!