Is there a material that I can lightly plate copper onto and wash it off?

If your sole intention is to recover pure copper from a solution of copper sulphate - there is no need to go to the complexity of electrolysis.

Place an iron nail into the CuSO4 solution. - That is a pure iron nail - not a nail that is galvanised or coated with tin etc,

In a few minutes pure copper will be deposited on the nail and bottom of the container . Filter the copper out of the solution . You have recovered pure copper. Easy.

You could paint just about anything with electroconductive paint and then burn away the substrate. Seems easier to just buy it. Copper wire is 99.9%, generally.

I don't think so.

Start with a thin wire of high purity copper and plate onto that.