yes sir, you hit the nail on the head. it was super fine and no matter how many times I brushed it came back.According to the CYA chlorine chart you should be above 5FC @60 CYA. With a target of 7-9. I'd do a SLAM, be and then stay@ 7FC or above and that should clear up the green.
Likely the "dirt" it's dead algae. Is it super fine? As in lightly disturbing the water near it stirs it up?