I would say that the first run through with VERY small increments in depth is a good idea. Be cautious that you don't make the depth changes so small that you only succeed in heating up your cutting edges more.
There is a known balance on cutting blades of any type and the rate of cut that keeps them sharper and cooler. I don't have the figures for copper as I do most of mine by hand.
I would very much like to see simple forumla's or table for RPM, end mill size, flute number, rake angle with recommended feed rates.
That to me would be a GEM of information.