Is it possible to rent a bike in California (SF ideally) and drop it off up north somewhere (Eureka ideally)?
I see a few options, like in the comment on the question:
Rent a bike at your start point and cycle to your finish point, have someone send it back for you, a bike shop will likely both have the packaging materials and the knowledge, and often the contacts to send it for you.
This can also be done the other way around, renting where you finish and have them send it for you to where you want to start. Rental companies may prefer this as they can eye the bike when you hand it in rather than relying on an other company to accept it to them.
If you have a driving license, rent a bike where you want to start and ride it to the finish, rent a car/van which is suitable to transport the bike and drive it back to the start and yourself and the rental car back to where you rented that.
Alternatively, buy a bike where you want to start and sell it once you have reached your finish or bring/send it home if you like the bike.
And of course, with cycling getting more popular you may find that there will be companies doing the long distance rentals in the future.