This is what I did and my problems concerning algae were worse than yours and now my tank looks nice (except for stupid microbubbles in the water column).
For Aiptasia use Aiptasia X or one of those zappers. Aiptasia X is cheaper though. Some people even use military grade laser pointers, C4, whatever floats your boat.
I did the following consecutively:
1. BRS GFO reactor and started using it (rinse GFO before adding to tank!!!).
2. I Tossed some High Quality carbon into my sump/filter.
3. I added some dry macro rocks to increase surface area of biological filtration.
4. Feed fish once a day, and make sure not a single piece gets wasted, I shed tears when food hits the sandbed.
5. Using a scraper and your hands to get as much algae out as possible. Turn off the pumps/ flow. Use a toothbrush and scrub really hard on the rock where the thickest algae is attached.
6. Use a net to get the now free floating algae out of the water column, as much as possible.
7. Do a 33% water change and vigioursly get into that sandbed with it.
8. Clean out filter media and set protein skimmer to skim wetter than usual.
9. Add some nitryfying bacteria, this is very important because this process will be rough on your system
10. THREE Days of Darkness, sounds crazy but it works even as a stand alone it can help. Use towels and clothpins to cover up your tank, turn off the light timers, should be near pitch in there , maybe a sliver of light in one corner. Your softies will strecth out a lot but they will revert back to normal two days later after your done. Your sps will be fine, I have monti, acros, birdsnest, lps, shrooms, and even an rbta. During the three days continue to add small amounts of the nitrifying bacteria.
11. After the three days are up I uncovered the tank, I played that song "reunited" by peaches and herb, do one more water change! replaced gfo and carbon! added bacteria! feed fish once! Never looked back.
Just stating what I did.
