You definitely have it for it to be spreading around like that.
Any chance you're willing to try a UV filter to see if that keeps if from spreading while you're putting the effort in to knocking it back?
I don't see a lot of coraline in these photos either....that should be taking real estate from the green algae over time. Is that just my view through the photos or is coraline lacking??
It's my understanding that you need a massive UV filter to make much of an impact? I won't rule it out, but definitely not my first choice though, for obvious reasons.
The tank is loaded with coralline, the algae is actually growing on the coralline that's encrusted on the back of the glass.