Feeding anthias can be very challenging. I've only kept flavoguttas, ignitus, and ventralis anthias. All of them with some success. I would say the best success was with the ignitus. I eventually got rid of them because I wanted to keep flavoguttas and ventralis which I still have.
I started to get them feeding in all the same manner. First I made sure there wasn't many fish if any at all in the tank before them. I started them on reef nutrition tiger pods, they seemed to all love it and it immediately gets their interest. After a few days or up to two weeks of this (shorter the better since it's very expensive), I'll try to feed them hikari frozen mysis finely chopped up and or frozen cyclopeze. Good water flow like one would have in a sps tank will create nice movement for the food and once they're feeding on the tiger pods and taken them aggressively I've had good results in getting them to take the frozen mysis and cyclopeze. I didn't really prefer the cyclopeze cause much of it would get filted in my sock and clog it too quickly. Some of the ignitus would take pellets, but not all of them. The flavosguttas would never take pellets. And the ventralis will take them.
For your situation I would be worried about getting anthias that are known to be difficult feeders. The chromis are quick and aggressive eaters, and most likely will not give anthias the time they need feel comfortable feeding. If you really want to put the odds of keeping anthias on your side, I would remove the chromis. They're cheap and you can always get them again in a couple months once your anthias are all settled in.
Good luck, do a lot of research on anthias before you take the dive.