skip the hot water
no additional cost, and it will force less water use.
From my plumbing classes.... the 3/4" is to provide sufficient volume for multiple points to be in use without suffering a significant pressure drop. Copper also is anti microbial and therefore is a health +. Pex is plastic and at best is health neutral. Pex is easy to run, if the shower is the only place you care about hot water, just do a run to that and leave the copper to the rest of the bathroom.
Whats the projected ROI of this project? how many years to pay back the cost and time?