Nick....where's the fun in all that? Smith says it right.....take the scenic tour....stay in good VFR...fly down where you can see something....fly it like it is a helicopter and not a turboprop airplane.
Saving one fuel stop on a flight like this seems the lesser of the priorities....as does the hassle of dealing with major airports when there are hundreds of small airports that will treat you like visiting royalty and who will really enjoy seeing a 76 on their ramp. I found that to be the way to maximize the opportunity of crossing this grand country by helicopter. The view from 7,000 feet (when it is above actual ground level) is not much different than when sitting in an airliner peering out the wee window.
As to IFR....last time I checked clouds all looked the same from inside them no matter where in the world I was.