In the past, I had ordered a pre-quarantined CB online from a reputable dealer, assuming that it would have had to have learned to eat from the water column during the QT process. I had every type of food available, live black worms, clam, Masstick and assorted fish foods. I even made a DIY CB feeder, with all the holes drilled into it, but it didn't take to that either. The only food I offered that it ate was Masstick, which I applied to porous rock and froze prior to adding to the DT. It liked the Masstick, but that wasn't enough nourishment. The fish would never identify food in the water column and it perished in 3 weeks.
That was a tortuous process that I did not want to put another fish through, until one day, while at the LFS buying supplies, I noticed a nice looking CB and mentioned it to the LFS owner. She indicated that he had been "eating like a champ", so I had her feed him and sure enough, it was an aggressive eater of PE mysis. So, I took the chance and purchased the CB.
I put the CB thru a quarantine process, which included feeding with Metro, applying
Copper Power & then Prazi. It continued to eat PE mysis thru this process and I slowly started adding LRS Reef Frenzy to its diet. After the quarantine process completed, I put the CB in my DT and he's still thriving 3+ years later, with an assortment of other fish that pretty well equals what you've listed.
My CB will only eat frozen foods. Never took to clams or live black worms, but loves LRS and PE mysis and has recently taken a liking to chunks of frozen bloodworms. I feed broadcast style, without shutting down my wavemakers. This moves the food throughout the tank, so there's less competition in the feeding spot. As the CB tends to eat at the top of the tank and the other fish prefer the mid and lower levels for feeding, my CB doesn't have too much competition for food. But, while I feed frozen food, I'm focused on dropping the food when my CB is ready for it and not too much at once, as they tend to get confused if they have too many targets to eat at once. So, I'm primarily feeding my CB and as he misses quite a bit, the rest of the tank gets his leftovers. I also feed frozen twice a day, sometimes more, as CB's have small stomachs (as they're built to hunt throughout the day) and even a single feeding per day wouldn't be sufficient for it to thrive.
So, I strongly advise not to buy a CB without witnessing that it is an agressive eater, as some will never learn to eat from the water column. You must also be willing to commit to feeding it multiple times per day and as they typically only eat fronzen, that can be an unrealistic commitment for some people. I also agree that it's best to initially give a CB a separate tank to learn feeding practices & food types, away from the DT and competition. In my case, the quarantine process served for this. If you don't have a 2nd tank for this and you have a large enough sump with lighting, that may suffice. I would not leave a CB in an acclimation box for long, as their natural desire to hunt the reef would work against you in a sterile, empty acclimation box.
A CB is a wonderful fish and mine certainly is my favorite in my DT, as they have a great personality! Just do yourself and the fish a favor, and don't buy one without knowing that it will eat from the water column!!!!
Good luck!!