A little late to the conversation, but -
In my experience, berghia really aren't the best and most reliable way to eliminate aiptasia. They're good at getting a population down to where you can manage it through other means, but they won't completely eliminate an infestation. Additionally, the initial berghia that you bring in are almost never enough to take down the aiptasia alone; they need to start breeding in order to take out a sizeable infestation.
Looking over your inhabitants, the dottyback, flame angel and coral shrimp are all potential predators of adult berghia. The hermits could attack the eggs - in addition, if you have amphipods or bristle worms in large quantities, those are also known to eat berghia eggs. I have a 20g tank that was completely overrun with aiptasia. No adult berghia predators, but no matter how many berghia I put in that tank the aiptasia never decreased. I'm 100% sure that their eggs were being eaten before they could hatch, so a breeding population could never get established.
In my larger tank, I have a pyramid butterfly that dispatches aiptasia with abandon. Once a visible aiptasia pops up, it's usually gone within a day or two. He's not completely reef-safe when he gets too hungry, though - I have caught him nibbling on acans and similar corals. I now put a sheet of nori in the tank every morning, and that seems to distract him from nipping at corals.
In the smaller tank... I was eventually able to temporarily get the aiptasia under control with an aiptasia-eating filefish, three peppermint shrimp, and a UV torch. I had a heck of a time getting them to start eating the aiptasia, until I started pre-cooking the aiptasia with the torch. Once I did that, they started eating the aiptasia on their own, eventually moving on to the aiptasia that I hadn't pre-cooked. But after that outbreak ended, a few aiptasia were left in inaccessible places, the peps died, the filefish lost his appetite for aiptasia, and I got out of the habit of blasting the aiptasia with the torch, and now the tank is overrun with aiptasia again. Just started back on the treatment earlier this week and the filefish and my new peps are eating aiptasia again, so hopefully we can get it all beaten back again.
