I found the copper to be the most difficult. Thicker and harder were easier to get straighter, and I was spending a lot of time bending wires. My copper was a little smaller than yours, and my steel was a lot thicker.
How long of sections did you do? did you cut 4" sections, or many feet at a time? I wasnt able to completely remove curve, but if you spend enough time with it, it gets fairly straight. When using the music wire, its very straight, and doesnt get bent while working with it. But its very difficult to solder, comapred to copper or gavlanized steel.