I think you should keep the filter running with NO backwashing until there is very little flow of water back into the pool. That will help focus your time with getting your pool cleaned out. Skimmer socks work well and they are cheap. They do keep gunk out of your filter. What you really need is more chlorine - if I understand right, your CYA is 70, and your FC is only 1.5. To kill the algae, you really need to get your FC (free chlorine) level from 10 to 20 ppm and keep it there (see link. (By the way, the beauty of Ben's kit on poolsolutions.com, is that it lets you measure free chlorine levels over 5 very easily). Onxe the algae is gone, you should run the pool at around 5 ppm of Free Chlorine.

Also, what other (if any) pool cleaning equipment do you have? I don't have a waste line but don't really miss having one. I use a leaf eater hooked up to a garden hose with a fine mesh bag to get gunk out, personally. Once the gunk is out, your regualr vacuum should work just fine.