Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Augusta, Maine to Caribbean as you normally would.
For a flight from Augusta to Caribbean, you will be flying from Augusta. Augusta (AUG) is just 1.1 mi from the center of the city.
Yes, there are multiple flights from Augusta, Maine to Caribbean for under $700. The cheapest flight booked recently is on JetBlue for just $636, but on average you can expect to pay $1,002.