Algae is a chemical problem, not a filtration problem. You can have the best filter in the world, and without enough chlorine you will still get algae.
There's only one reason for algae growth, and that is the lack of enough free chlorine (FC) in your water to prevent it.
Once the algae is dead, a better filtration system will help to clear up the cloudiness faster, but only chlorine will kill it.
You say you have been SLAMMING, but your test kit only measures chlorine up to 5 ppm, and that's total chlorine (TC), not just FC. Some portion of that is likely combined chloramines (CC), meaning your FC is probably even less than whatever you are measuring. TC = FC + CC.
The FC level for a SLAM is 12 if your CYA is 30 as you said. You do not have any way to tell if you are anywhere near that. And obviously you must not be, otherwise your pool would not be green.
I understand your reluctance to spend the money on a test kit, especially this late in the year. But without one, trial and error is about the only other tool available to you. You could drain the pool again, add CYA to get back to 30 ppm again, then double the amount of bleach you were adding daily this last time. I hesitate to make such a suggestion, because your FC level could get dangerously high that way, but without a good test kit, I'm out of options for you.
BTW, how much bleach have you been adding each day? And what strength is it? Is there a date code on the jug anywhere, like 15123 or 2015123?
