It is safe to swim at slam level, however we don't recommend swimming until the water is clear enough to see the bottom of the pool. We want you to be able to tell if someone gets in trouble in the deep end so you can find them easily and get them out. Not trying to employ scare tactics, but there have been documented cases of drownings in murky public pools where you couldn't see someone who had sunk to the bottom.
The dusty piles you see are the dead algae. Think of them as little piles of victory! If you slowly vacuum to waste every day (or as close to daily as you can) you will help the water to clear. All that dead algae must be filtered out for the pool to clear. One great way to document progress is to pick one location in your pool where there is a landmark like looking down the pool steps and take a photo at that spot every day. You may think you are not making much progress day to day, but when you compare the photos you can see how the water is slowly clearing.
As for copper, TFP has collected anecdotal evidence and some of our members with extensive chemical knowledge have experimented with various copper removal methods. The bottom line is that there is no filter that removes copper from water. There is no chemical that removes copper from water. Sequestrants will temporarily bind the copper and keep it in suspension so it doesn't deposit stains on pool surfaces. Sequestrants gradually break down in chlorinated water in about 4-6 weeks and must be re-applied to keep the copper suspended. To get rid of copper permanently the water needs to be replaced with a partial to full drain, depending on how high the original copper level was. To avoid future problems with copper, check all the active ingredients of any pool chemical you use. Almost everything that has "blue" in the name has copper as an ingredient. Many algaecides contain copper (one reason why we don't usually recommend them). Mineral products that tout lower chlorine use usually contain copper or other minerals you don't want in your water. Copper can also be introduced into a pool via extremely low pH water eating away at the copper heat exchanger from a pool heater. Copper is not usually found in city or well water.
You have reached the cloudy blue stage and that is great! This is were POP (pool owner patience) pays off. Stay the course with the slam until all 3 criteria are met.