Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Portland, Maine to Kyoto as you normally would.
For a flight from Portland to Kyoto, you will be flying from Portland. Portland (PWM) is just 2.9 mi from the center of the city. Portland is the only Portland airport and it handles 0 outbound flights to Kyoto per day. 1 airline has flights to Kyoto from Portland on a regular basis.