Hello,
First sorry about the tangs I know that is hard believe me. I have a purple tang and tommini tang and they do great together in my 240g along with my Naso hippo and Lt tang. I have found with my experience that tangs are kinda introverts. May I suggest this, make sure your 240g has cycled for 6 weeks min, then do not add any other fish at all, except the tangs.
When I had my 125 I tried to add a yellow tang hippo several times and they never made it. When I went to my 240 I kept my old fish but, I added the blue hippo first (most sensitive), then added my Naso, then Lt tang, then tommini then purple in that order. Of the bunch the leader is between the Naso and Lt tang, then blue hippo. My purple tang and tommini tang I swear are dating. They always stay right next to each other and both stay in the same rock cave.