I am not familiar with anthias, nor melanurus wrasse. I have a sixline wrasse and never had any problem with it. It is in my larger tank, but I used to have one in a 50 G tank.
the cardinals are not very active fish, but they are out on the open. My 2 pajama cardinal are ok together as the chasing is minimal, they are in my 40G tank along with firefish and scissortail.
But when I had 3 bangai I ended with only one. Also they did not live very long.
For schooling in my large tank, I have green chromis, but to avoid them killing each other you would need a minimum of 6, which is probably to many in your tank. I have 7 for about 5 years. you could of course get only one.
Size wise and for a beautiful fish you could consider a coral beauty angel or an Eibli angel ( this is what I have), but I do not have any corals and I do not know how they would be with corals. My guess is it would depend both of the fish and the corals.
My 2 scissor tail are always out, I also think that if you had more than 2, like 3 or 4 they would be less likely to hide. They do not fight with my firefish. They do hide at night.