Sorry, unlike AA, UA hasn't had power in the economy cabin until the introduction of the p.s. product. Since your flight options did not include p.s. flights, you'll need a well charged battery and maybe a back-up one too, for your transcon trip.

If your flight is operated by a 767-200 aircraft, there's not even a benefit in upgrading to business class for power, as the 762s do not have power either. If it's a 767-300, you would be able to use an empower adapter for an AC connection to your computer.