I would hazard against removing your rock. I am very much an "ecosystem services" minded guy and that rock is doing you a whole lot more than just growing algae. Swap it out and you'll probably have dino's take the place of the algae, then have the algae come back after you best the dinos.
I would tackle this by significantly ramping up your CUC, for a 90 check into
this.
WAY cheaper than going through your LFS. Let them go to town for ~3 weeks then reassess. An urchin may be the next move after, maybe conchs, perhaps an algae blenny, it all depends.