I looked up the friction loss in 3/8" Type M copper and 3/8" Pex. With copper at 3GPM the friction loss causes a pressure drop of .168 PSI per foot. With 3/8" Pex at 3 GPM you lose .541 PSI per foot. However, with copper you will have fittings that will cause additional loss depending on the actual fittings and the number of fittings. 90 degree vs 45 degree etc. If you use Pex in a home run configuration you eliminate most of the fittings. I suspect the higher friction loss in Pex is more of a result of a smaller inside diameter as opposed to rougher internal finish. So for your shower plumbing in Pex at 12' of run and 2.5 GPM flow you should be looking at a pressure reduction of about 4 PSI. On a fifty foot run at 3 GPM you are looking at a 27 PSI loss.
Pressure loss = Friction Loss per foot @ Flow rate x feet.
Flow pressure = Static pressure - pressure loss
The other thing you need to consider is pressure loss due to elevation. Probably only about 1/2 PSI if you are only going from basement to first floor.
This site has all the information and examples for setting up Pex systems. This is where I found the pressure loss chart for Pex plumbing.
I know you are working outside the box but there is a lot of good information there to help you make your decisions.