I'm a little confused by your pool volume. In an earlier post you said it's 36,000 but now you say it's 56,000. Maybe a typo? Given the dimensions of 20x40 and averaging a depth of 5' we'd be looking at +/- 36,000.

Would you please post your test numbers?

FC, CC, TA, CH, CYA, pH, and please describe what you use for water testing.

It sounds like you've been doing everything right as far as brushing, backwashing, filtering and treating the water. Knowing the FC and CC readings would help us try to understand what's going on. If the water is still cloudy we might be looking at issues unrelated to algae.