Unless an expert knows better, it would be very, very sketchy to deduct non-rev mileage that cost you nothing. A mileage deduction assumes you're incurring costs.
I think you should give up on mileage between home and drill site, the nonrev makes it too hard.
I think you could deduct the cost (or some specified percentage) of the rental car + gas. Rather than one-way mileage, it's a cost incurred incidental to the duty...needed for travel from the airport, to/from berthing and messing, and possibly business-related in-and-around. Run it by your accountant.