I only have personal experience with a handful of algaes, and none of those has been as you describe. Many alga including bryopsis, caulerpas, and halimeda do attach very firmly to the substrate, but I wouldn't guess those from your photos.
Your best course might be to get a definitive identification from a laboratory. I don't know if U of A has schools of marine biology or botany, but if so they might have a lab that offers this service. UCLA, UCSD, and USC are not that far from you and one or all of them should be able to help. Purdue University, which has no marine-related schools but does have a large school of botany, was able to ID some algae for me several years ago. They charged $10 and had an ID for me in a couple of days.
Meanwhile, your infestation does not appear to be of epic proportions at all, and you're on the right track in reducing your nutrient levels. Alga require very little nutrient to survive, but once the levels drop below their tolerance threshold they die back very quickly.
There is no magic bullet for this, but more info on your system might help pinpoint ways to further reduce nutrients that are fueling the algae. And if you can get a reliable identification, then you might find more useful information in a different or new thread.