I have a big Aiptasia issue in my large system, and I know you mention no chemicals, but Red Sea Aiptasia X works if you use it correctly. I’ve just used a whole bottle in one go and it works fine. They don’t generally spread.
Ive also introduced 30 Berghia to get to all the difficult to reach areas (its very deep!)l they work, but are expensive and I know you mention there maybe not an option so I appreciate that.
There are the fish you mention and I have a Copperband but the problem is it’s very hit an miss and depends on the individual etc.
Assuming you can reach most of them, the best method I’ve used is Aiptasia X