I learned the hard way as well about quarantining fish
By the time I was done with leaving my DT fallow it had been fishless longer than it had fish in it.
By far the best treatment for ich is hyposalinity and sadly, you don't have much of a choice but to QT them all at the same time to do the treatment. You might look at craigs list to pick up a cheap used tank but that's about it. As for the compartments, I would advise against it. Tight spaces can be stressful for fish, especially tangs; and that is the last thing that you want.
Turning the lights off and warming the water doesn't help against ich in salt water the same way it does in fresh.
However, if this isn't a reef tank and you have 0 inverts then it's possible to do the hyposalinity in the DT and just get it over and done with. Another possibility is to remove all the coral and inverts to the 40 so you can do the hyposalinity in the DT. There will be people that will argue with me about this but a change in salinity isn't dangerous to bacteria so it shouldn't hurt your bio filter although it might kill any hitch hikers on your live rock causing a potential ammonia spike.