Jesus--I wouldn't get ride of the rock. Think of how far you have come with battling this algae. Too just get rid of it at this point would be like cherrying up an old car and selling it for less then what you put into it.
I would add some dry (not live or "dead") base rock to the tank to further improve the look of the tank. This way you can cycle it and further improve on the aesthetics of the tank. Believe me, this will not be the last time you re-aquascape the look of your tank. We are in a constant "flux" with our systems.
Also on a side note, a little hair algae is beneficial to a tank IMHO. Some tank inhabitants graze on hair algae such as tangs, blennies, angels, snails, sea hairs, hermit crabs, etc. If you look closely at some of the pics from the oceans reefs, you will notice that there is hair algae (and cyano at times). It is as much a natural part of the reefs as are fish and corals. We have become "accustomed" to view our tanks to be "pristine" as we can possibly get them.
Thanks!