Going back over things...
The purpose of a QT, is to prevent any diseases
from entering your display. Some people treat their fish regardless if it's actually sick or not, but I only treat if I see other sick fish at the store (or an unknown online purchase) or if the fish does become sick. If fine, they spend 4 weeks in QT, then into the display. If they become sick, it's 3 weeks of treatment, then 2 weeks of observation, then either extend QT if I don't feel comfortable with the fish, or into the display.
IMO, UV is useless against treating diseases. The main, and really only, purpose of a UV is to help kill nuisance algae (technology copied from pond keepers). It's also really expensive for an adequate sized UV for any tank over 100gal.
Going over your stocklist, fish that would work in a 20QT (and or also commonly available small), a small dogface, a small yellow tang, a small picasso trigger, and a small juvi Emperor angel, all would work in a 20, if kept by themselves, one at a time. A Harlequin Tusk though, usually are never available under 4", and 3" specimens are pretty rare. The Tusk is also the one fish, I would most strongly recommend QT'ing. One option here, would be to find a local Tusk for sale, that the previous owner has had for a long time (over a year) and hasn't added anything to the tank is some time. Still a risk though. Also, if you only purchase small other fish, as time goes on, and the girls mature, you could setup a larger QT then, and add the Tusk last. The smaller already established fish, probably would be fine with a larger Tusk.
A standard 65gal is half a 125gal, 36"x18"x22"