tranny cooler lines out of copper?

I wouldn't. Copper tube burst pressure usually derates as temps increase. What might have a 500 psi burst at room temp 70* could have a burst of 125 at 180*. Not much of a safety factor with trans pressures/temps. Add in vibration and stress hardening and it may not last long, especially in long runs.

Look around the net for burst pressure calculations ( Barlows Formula)