Unless you plan on drying out your rocks, just "cleaning" them probably won't have the effect you desire. I think it's more importatnt that you try and find the source of your algae, otherwise you'll eventually end up right where you are now. One thing is certain: you have a source of excessive nutrients that is feeding the algae.
Have you tried vacuuming your sandbed? A 4-yr-old sandbed that has never been cleaned could contain some nasty stuff. It might be the source of your phosphates, which in turn is the source of your algae problem. Personally, I don't vacuum my sandbed, but I do stir up small sections of it right before I do a water change.
I battled some bryopsis not too long ago. I siphoned out all I could and did some constant water changes for a 2-week period (5g water changes on a 75g every 2 days for two weeks). Took care of it. I read that someone blasted their bryopsis with boiling RO water and that seemed to kill it. Don't know if that truly works, but even if it does, you'd have to be careful about nearby corals.
Avoid overfeeding your fish, especially with flake foods.
A phosphate reactor is a good investment, but it is another expense.