At this point you are so infested that I don't think a 100% natural method is available to you. While a copperband is a good idea as you well know Aiptasia will multiply on you fast.. Each one of these can generate more by simply letting a piece of itself go.. I would personally take an extremely aggressive approach if I were you.
I'd take out all of your rock, place it into tubs with saltwater, heat and circulation and then leave a few pieces in the tank. I'd then use mechanical means to inject all of the larger Aiptasia and then place like 12 juvenile peppermints into the tank to take care of any small ones that they can reach. If you want to use a copperband thats up to you. After those rocks have sat in your tank for like 4 or 5 days and you don't see any more of the little reef wreckers I'd place them into a new container with saltwater, heater and circulation.
I'd keep repeating this process until your rock is clean. You should then be able to safely place all of your rock back into your tank and hopefully it will be pest free.
There are also other methods out there like 1 tsp sodium hydroxide with 2 tsp kalk in 100ml distilled water which some say is a sure fire way to rid yourself of them.. I have not tried this method, but have tried boiling water, lemon juice, kalkwasser and joe's juice. The key to the latter is that you have to dribble it over the tentacles very slowly until they in-jest some of the product. Then follow them back as they start to recede and cover them with joe's juice or kalk paste.
Hope that helps.