If it's your show, yes fly it high for all the advantages you mention. A west-to-east in the winter should probably get you some pretty good tailwinds and if flying in mountainous areas, extra height above the peaks and ridges when crossing them is your friend in terms of turbulence avoidance.
You might compromise with the other guy when it comes to a leg or part of a leg that's scenic and where turbulence isn't a factor. Seeing the sights helicopter style is best done at a reasonably low altitude.
When you are planning on going places like an airplane does, it's best to plan on flying it like an airplane is flown: get on upstairs, set an appropriate cruise power, and enjoy the benefits. Those who insist on flying helicopters hundreds of miles cross-country at 300 to 500 feet AGL because of possible emergencies are (in my opinion) engaging in some needless dramatics.