First, do you have a lot of trees and vegetation over the pool? If not the safety mesh should be fine. I've been using one for 10 years and the only time I open to algae is when I open late. But if you have a lot of detritus falling on your cover a solid cover may help: Caveat: Solid covers fill up with rainwater so unless you have winter pillows underneath prepare to pump it clean with a cover pump regularly.

Second: FC of 3-5 is meaningless at this point. Sorry to be blunt. If you have algae you must clear it out and shock and re-shock until the algae is dead. FC= 3-5 is only useful as a maintenance level of free chlorine, and only when your stabilizer level (AKA, CYA) is between 30 to 50 ppm. IF your CYA is there, then you shock by raising FC to 15ppm and keeping it there. But if CYA is higher, FC=3-5 won't be sufficient for maintenance. That's why I said it's meaningless.

Third: The BEST algaecide, by far, is chlorine. It's also the cheapest. We only recommend one algaecide: Polyquat, sold under many brand names. Polyquat is good as a preventative and acts to clear your water as well. It's good stuff, but pricey and NOT what you need.

I think your real problem is how you close and when you open. Opening for filtering and chlorinating should begin well in advance of opening for swimming. Since algae growth is inhibited when the water temp is below 60deg F (Please, others, correct me if I'm wrong on the temp) when the water is close to or above that you should start opening. When I open properly, I open to clear water (and a lot of dust on the bottom). When I open late, I get algae and green water.

In the fall, I try not to close until the water is down to 60, though I usually have to start when it's just below 65. I shock the pool, make sure it's algae-free, add a quart of Polyquat and wait 48 hours. The Polyquat drives the FC down. I then raise FC back to the shock level and shut down the pump and close.

I hope this helps.