You'll have to make a good business case to the owner. Such arrangements can be made. What the owner is seeking to avoid is their rental aircraft not available at home to create revenue for 6-8 hours a day, while it's far away creating only 2-4 hours revenue a day in rental. While the plane is far away, the cost and effort to rectify a problem increases exponentially.
So you are best off presenting the idea to the aircraft owner as good business for them. Said differently, offer a good daily minimum regardless of use, and a deposit in case there is a problem far from home.
A long time ago, I asked to rent the club's Cardinal RG for a week. The answer was: Minimum 4 hours rental payment ($55 per hour at the time) for each day, flown or not, and above that whatever I flew. My average was 3.9 hours per day, and they were okay with that. On another occasion, when I did damage their 172RG just a bit, I paid to fix it. My mistake, not their problem. That seemed to help their respect for me as a client.
The profit on a rental aircraft is meager. It will be instantly eaten up by a minor "event" far from home. With the aircraft a half continent away, a stuck exhaust valve, or dented wingtip becomes a big deal. Have your plan in advance for how such an event does not become their problem. As perhaps a non citizen, it's probably very difficult to buy the plane for yourself (and not your plan anyway) but offering a large (enticing) damage deposit, as though you'd bought a part of the ownership is a great way to advance your objective. Consider that those who did buy the plane for such trips do take those risks entirely upon themselves (yeah, I've had a stuck valve in my plane a thousand miles from home).
The California to Alaska route is very demanding (weather and topography). Totally scenic, and demanding (there are a few photos in the photos thread). Aircraft owners know this, and will be wary of their aircraft flying that route. Recognize the vital need for a comprehensive emergency kit (many hundreds of $ and many tens of pounds) which the owner has not planned to provide.
Those who fly these demanding routes likely have heritage doing it - friends who have done it, and offer advice, or better, they have flown as second pilot beforehand.