I was having the same problem at the beginning of this summer. My free chlorine was losing about 1ppm overnight, but since I live in the woods I considered it ok. I kept my chlorine level at the high side of shock levels for my cya. I don't normally use algaecide, so I just kept the chlorine high but my water continued to be slightly murky - I could see the bottom, but the water was not that "crystal sparkly look" . I decided to add algaecide 60 polyquat, and the water cleared up overnight. Even though I had no combined chlorine, and kept the pool at shock level, there must have been something going on. I have no real answer for why this worked, but it may be something for you to try. I was thinking it may be my filter too, so I know where your head is
The polyquat may be the cheapest thing to try first
Keep us posted
Just another thought -You didn't post your cya number - If you cya is too high, your chlorine level may not be truely high enough to kill all of the algae, therefore the algae will keep growing, just not fast enough for the water to turn green.

Just another thought -You didn't post your cya number - If you cya is too high, your chlorine level may not be truely high enough to kill all of the algae, therefore the algae will keep growing, just not fast enough for the water to turn green.