First off, amazing tank. One of the nicest nano's I've seen. Vibrant colors and very nice growth. I inspire to have a 55g with as much color as your's.
For the aiptasia problem, there are three possible ways that I would go about it. There are chemicals of such like aiptasia-X or Joe's Juice that are suppose to do the job very well.
Another option would to simply chip away a piece of the rock that has the aiptasia on it. Would not suggest it for your tank for obvious reasons but it worked for me when I found my first one growing.
Last thing I have heard is to either boil water and squirt it at the aiptasia or take the whole rock out and boil it. Not very intelligent due to the fact that it obliterates everything on the rock but it works for rock with little to no growth on it.
My best suggest would be to go at it with the aiptasia-x or Joe's Juice. Let me know how it works out for you.