You must love playing with fire. Most of those fish you mention are among the most susceptible tangs there are when it comes to ich. That said, I do like your taste as the Achilles and Powder blue are among my favorites as well but those are known to break out in ich easier than any other tangs. Purples are also really sensitive to it. Further, a UV filter will do nothing for preventing ich. The only thing the UV will do is reduce the parasite numbers in the water column. It won't eliminate it nor will it control it. The only time a UV is effective is when the parasite is in the trophont or theront stages which is when it's in the water column. Those stages last a very short time and not all will make it through the UV. In fact, very little will compared to what will be on or in the fish or in the substrate. Regardless, the cycle will repeat as long as there are fish to host.
Having said that, I'd be reluctant to have that many of either the Powder Blues or the Achilles or even the purples. Despite the tank size, they are likely to squabble and fight which will cause additional stress that could quickly lead to a full blown ich break out and with a tank that size, removing fish is very difficult which necessitates the need to choose the fish and number of species wisely. Especially if the fish aren't being treated with therapeutic levels of copper in QT for the appropriate time.