Just to clarify my original post:

I won't be moving the H & C copper supply pipes so installing the new
faucet set upside down will not change the sides the Hot water is on.
It will still be on the left side, but the hot water will go through
the part of the faucet which was designed to handle the Cold water IF
the set was installed in the conventional manner.

The valves in the new set both open in the same direction.

Aside from some brands' H & C shower stems opening in opposide
directions, is there any other difference between the H & C stems on a
given faucet set?