If you have a patient travel agent who enjoys the game, try buying a round trip to one of the Korean cities that served by KAL out of Haneda airport, routed as follows:
March 20 SFO-NRT on United
March 21 HND-Korea on KAL
May 21 Korea-HND on KAL, stopover in Tokyo
May 22 NRT-SFO on UAL
Don't use the March 21 and May 20 tickets.
Because you are changing airports in Tokyo, you will get your bags back at Narita. And because KAL isn't United or Star Alliance, on May 22 UAL won't know that you didn't take the March 21 or May 20 flights and won't cancel your May 22 return ticket.
As Jgish noted above, USA-Korea round trips are usually cheaper than USA-Japan rount trips.