Tonight was my catch up night on some old threads. I have found a connection in your thread and Prop's thread as well. lol Unfortunately, both involve some of the struggles of this hobby.
I have tried everything for aiptasia... I would show you how bad my tank is but its embarrassing. I will give you my experience on each of the natural methods. I have tried kalk and it had the same effect as you experienced with aiptasia-X - massive growth later on. I later found a thread on a guy who cultures berghia who said that he uses that method to propagate his aiptasia. So I have turned to any other method and am reminded that everything you read on the internet is not always the answer. In this case, I think its a good solution for 1 aiptasia, but I believe the same solution becomes an issue when you are looking at much higher quantities.
First, I tried berghia. They only eat aiptasia so how could I go wrong? Well.... those guys are expensive. I do believe they can do the trick, but I never established a large enough population in my main tank. I also believe they don't acclimate as well as other inverts. The vendors didn't lie when they said you would never see them again in your tank, unfortunately, 6 months later and I still don't have any dent made in my aiptasia. I spent over $300 to get a large amount for my display of adult sized berghia and never saw them again. I also bought juveniles and adults for a biocube to try to get them breeding and they did well, but my travel schedule did not allow me to breed them well. This is the way to go with berghia if I ever did it again. It also requires you to isolate the anemones to feed them until you have a large enough population to really attach the main tank.
This caused me to turn to every other method I know. Fish and shrimp. I had success eradicating my first saltwater tank of aiptasia with peppermint shrimp. I just find that in the display tank environment, they get lazy and choose to eat the food you feed over searching for aiptasia at night.
I also have had 2 butterflies and 2 file fish. These guys are in a separate tank. I learned the hard way that filefish may eat peppermint shrimp so I will no longer be doubling up on my attack - at least in the same tank. The video posted by Dkeller looks interesting and I may give it a try - with the peppermints and filefish. The filefish eat mysis pretty well, so I may end up hand feeding aiptasia and letting them go after the food. If it works for one, I don't see why it wouldn't work for the other.
The other thing I have had success with, moreso than the filefish, is butterflies. I had a klein's for awhile and also a long nose. Both of them did better than the filefish I believe. The only issue is that they are picky eaters and I lost them shortly after getting them. My second shipment arrived DOA so I am picking up another set tomorrow morning (along with additional peppermints). I keep going back to these guys as I was able to clear 2 fully infested rocks in 3 days. I have had a few pop up on those rocks since then, however I am positive if I can keep them alive another go at it with those rocks would take care of it.
I wish you luck. I also have the issue with cyano and I have not read far enough back in the thread, but it appears you have read the article that links the two issues together. I am gathering this based on the "imbalance" discussion - I tend to remember an article that addressed both aiptasia and cyano as a nutrient imbalance. I will tell you, that the few pieces of live rock I was able to get clean of aiptasia have remained free of cyano for 3 weeks. This is after being returned to the display. My display tank has the highest flow of any of my tanks and they are all 1 system. Neither of the frag tanks (1 has corals and the other has these unsafe fish in them) have issues with cyano even though they have lower flow and similar lighting (I run T5s on my display and frag tank and the fish tank has a chinese LED fixture over it). All of these tanks have plenty of lighting to feed cyano if it wanted to grow. My display is the only one with the issue. My display is also the only one that gets sunlight exposure however I am not willing to say that is the main factor, although it could definitely be a contributing factor based on the fact that many people are successful with the lights approach. (I have done this as well - it was only temporary relief in my experience).
Where does this mass of words leave us? We all struggle together in this hobby. I hope that my rambling can help you move toward a better tank. I know that every time I pop into this thread I am either entertained or I leave with a little better understanding - sometimes both! Thanks again for taking the time to document your tank and share it with the rest of us!!
Cheers! Now I am going back to catch up on the rest of the stuff I have missed.