Carey, I'll try to help you out and let you know what my situation was. I recently got a pretty bad Aiptasia problem that I wanted cured. I was in your situation contemplating CBB, nudibranchs, chemicals, etc....
I went to my LFS and fortunatley saw a beautiful 2 YR old mature CBB they have had in their DT for a few months. She caught me eye. She was eating mysis and brine at the store, but I knew that didnt mean anything. These fish are so finicky once you start messing with them, changing environment, lighting, etc. Anyways, I bought her, took her home, acclimated and put her in my DT overnight when the other tank mates were asleep. I woke up and noticed the other fish were not "nice" to her. Her tail was nipped at, and her side was scraped up. Either from my purple tangs spear, or hitting a rock. So, I placed her in my QT/refugium to let her heal while I tried to get out a pesky Damsel and re-arrange some rockwork so when I put her back into the DT the other fish would be a little nicer. I put a rock that was covered with aiptasia down below with her for her to munch on, but she never even touched them! I tried to feed her clams soaked in garlic and she wouldnt touch them. Finally, one morning I woke up real early (4:30am) and went to check on her, when I realized she was on a different schedule than my DT. My refugium lighting comes on at midnight. So basically I was always trying to feed her during her "nighttime" hours. I got her to eat some mysis early that morning, and then she started eating like a horse! Her tail got better, and her side cleared up. I left her in QT for about one month and then placed her in my DT after I re-arranged it and got my Damsel out. After about a week I noticed that ALL of my aiptasia was gone, even the large one I thought I would have to use chemicals on. She is now probably my best eater in the whole tank and shes great to watch swim around. She's quickly becoming my favorite.
Long story short - you have to really take care of these guys and be very patient with them. Try different foods, etc. If you get a good, healthy one they will quickly become your favorite tank inhabitant. Good luck, and hopefully yours works out as well as mine did!