I have not read through all of the comments but it’s likely to me that If you have kept adding a new fish right away is your problem....
ich or velvet will remain in a tank for over 70 days (76 I believe) so what happens is the ich is likely falling off your fish (the little white spores) and as long as a fish is in the tank it can remain “in there” to totally rid your tank of ich or velvet (it could be either as tangs are susceptible to both) you need to leave your tank fallow for the 76 days.... to get rid of the total life cycle of it... (fallow means NO fish at all in the tank) you can keep your corals and cuc and shrimp and such as they are only carriers of ich and it will not effect them.... you will need to ghost feed the tank every now and then to make sure your snails and such have some food...
To treat your tangs in a qt/hospital tank you should do up to 2 weeks of copper... when you set up a hospital tank DO NOT put any rock or sand in it... you can use different shapes PVC pipes in the bottom for your fish to use as caves but rock and sand will absorb the copper and it’s too hard to keep it at therapeutic levels....
Also, it’s very important that when your tank is fallow if you add ANYTHING... coral, snail, shrimp ect you must start your 76 days back at 0 as all of those things can be carriers of diseases....
So my best guess (without reading the 3 pages of posts) is that you have kept fish in the DT after ich being in there... therefore it has always had a host to feed on (ich and other diseases can lay dormant for a while in the rock and sand but if there is no fish host it’s life cycle will end)
If you are treating to TREAT a fish with ich you may also need to do other treatments after the copper or CP treatment... ich can cause secondary infections in fish so I use the copper or CP at therapeutic levels for 2 weeks (you must test EVERY day because if it’s too low it won’t kill everything off and if it’s too high you will kill you fish... it’s a very fine line) Then I use the trifecta of meds... furan 2, metroplex and kanaplex... and do the water changes on the proper days (I believe it’s 25% every 3 days because of the way furan 2 works) and then that will kill off any secondary gram negative and positive infections.... I have had ich and velvet and done this regime in a hospital tank and all the fish have lived and are fine....
But again I think the most important part is you must go fallow for 76 days and rid your tank of any diseases that may be lingering....
People don’t qt and get away with it but it’s really better to just do it and then you can feel better about having a healthy reef.... that’s just again my best guess of what’s happening without reading the 3 pages lol