Z: are you sure that the drawer goes all the way to the back of the vanity? I would think the Mfr. left room for the plumbing.
I would do all new piping with pex.
i used copper in my walls, and plastic under the house
when i plumbed it, I sweated an adapter on the pipe before i shoved it thru the floor
then hooked up all from under neith. 3/4 copper to all fixtures, stubbed out with 1/2
1" from the meter to the heater
if your plumber is not familar with pex. find another plumber