1. Focus on flying the plane in a manner that uses as little fuel as possible not bothering to even glace at the fuel gauge, watching the air currents and gliding where possible.
2. Turn on autopilot and spend time and effort trying to calculate the fuel you have to see if you make it to shore before going back to flying as conservatively as possible.
Number 2 feels better. Number 1 is more likely to end with a safe landing.
If you have a deadline and won't be getting new resources any time soon, and what purpose does a estimate serve if you are already committed?