Clear green water can certainly be an indication of copper. Shocking would only possibly make the situation worse. I would try the seqestering agent according to directions--some require you to let your FC levels drop and lower your pH, some don't....also some work better than others...don't know if that is cause and effect.

If the green clears and the copper readings go down then you know you are on the right path

My question is where did the copper come from. If you put it there in the form of an algaecide then .6 ppm is not necessisarily that high. If it is coming from your fill water or pipes or heater then there is a problem. If it's coming from an ionizer...IMHO, get rid of the thing!