Well, I'm of the opinion you're probably going to always have some string algae on your waterfall as there's no fish there to eat it. I get this buildup and have to periodically scrape it down. I can't easily reach my wfall so I run a pole over the stone and scrape the string algae loose. It falls into a pool net I have waiting below and all is well for a while. I've also just blasted the stone with a hose and that will work to get any heavy buildup. I think this is a case of putting up with some inconvenience for a waterfall's sake. I know some turn off the falls, spray on hydrogen peroxide, wait 30 minutes and then hose the wfall down. Doesn't hurt the fish or plants and it's relatively easy.
I have a large bog filter and multiple pumps, lots and lots of plants, and even the stone overwhich the bog pours has some algae buildup. I also had this happen when my bioload was low. Algae is a plant and it's in every natural water source. I doubt you could get the nutients low enough to completely stop this from happening.
So I think making this chore easier is the better course, as a waterfall is worth it., imo.