Hi, and welcome to the forum!!
It sounds like you're not completely killing the algae before you let your chlorine drift down. With a CYA around 40, you need to run your chlorine level up to 15 ppm and hold it there not just overnight, but until you can go overnight without losing more than 1 ppm of chlorine. This usually takes more than one day....but it's the only way to really kill off the algae. You need to thoroughly brush the pool just after the chlorine addition, as well, with special attention to the places that you know the green is growing. Don't add anymore clarifiers, algaecides, or other goop--just plain chlorine will do the trick.
Regarding filtration problems--do you have a working pressure gauge on your filter? When you run your pump, does the pressure rise any? When you backwash, what color is the stuff coming out? You can check your filter (and with the treatment you describe it got during closing, I would!) by adding a handful of DE to your skimmer and watching the returns to see if it blows back into the pool. If it does, then your filter will need some work. If not, then the DE will coat the sand in the filter and will help it collect finer stuff than the sand would alone.
How are you testing your water?
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