Since you're able to identify specific spots where this algae tends to recur I wonder if you could try treating it with straight bleach? You could put some into a squeeze bottle (an empty mustard bottle, for instance) and squirt it directly on the spot. You could perhaps brush the area while you're treating it with the bleach.

This would be in addition to disinfecting the water and all equipment, of course. I'm just thinking that spot treatment, if possible, might be effective.