While it is admirable to approach your chief pilot, how about your union? DAL gives us deadhead for ocean crossings, but it certainly isn't out of the goodness of their hearts! It is only because our contract compels it. Here are a few clippings from our contract:

"No deadhead will be booked on the jumpseat."

"A pilot who deadheads on an ocean crossing flight segment, as scheduled or rerouted, will be (emphasis added) provided business class accommodations. If the aircraft is not configured with business class, such pilot will be provided first class accommodations."

Good luck in everything.