Your numbers look like you should see an improvement. Are you:
1) Vacuuming to waste once each day?
2) Brushing your walls and floor once each day?
3) Checking your FC level at least 2x, preferably 3x/day?
4) Backwashing whenever your pressure rises?
5) Double-checking your measurements, particularly FC vs CYA levels?

I like the skimmer socks because they are cheap and can pull a whole lot of garbage out of your water quickly.
If you sand filter is filled with sand, not Zeolite, you can try adding some DE powder (about 1/3 cup) through the skimmer and see if that increases your filtering capability.

You have to kill the stuff in your pool, and you have to get it out. High FC is to kill it. Brushing knocks it loose from the walls and bottom so the chlorine can kill it. Vacuuming, skimmer socks, DE, frequent backwashing are all to get the stuff out.