Well, getting 10,000+ miles wouldn't get the Plat Challenge completed (although it would do the Gold Challenge). So it's really just a matter of how to make Gold.
The easiest way (although not the least expensive) would be to book a pair of round trips JFK-OAK; if you pick your times, you should be able to get each r/t for $255.00. And since it's the same plane that goes JFK-OAK and then is just turned around to to OAK-JFK, you don't have to worry about delays, etc., messing up your connections.
Steve