With that many aiptaisia, I wouldn't do the kalk paste as it will totally throw off your calcium/alkalinity balance. It also burns any coral, anemone etc. it happens to get on (and it will get on something you don't want it to). For me, Aiptaisia-X has worked the best of all the commercial solutions, but there are always going to be little ones you can't see that eventually grow to a size where you can see them.
In nature, there is always some critter that eats some other critter you don't want and all have pros and cons. If you can go with the natural method I would, but there are some things to keep in mind.
Shrimp are a toss up. It depends on the species and the ones that don't eat aiptasia look like the ones that do so you aren't likely to know which on you've got.
Some fish eat them, like most Butterfly Fish or the Bristletail Filefish (Acreichthys tomentosus). However Butterflys are delicate and neither they nor the Filefish are completely reef safe.
Berghia Nudibranchs are probably the best option. But if the flow in the tank is to strong they tend to get blown away or sucked into power heads and overflows. And if that doesn't get them any wrasse in your tank will.
So, how you deal with aiptaisa _ and if you're successful - depends on the individual nature of your tank and what lives in it.