Go to the "Advanced Booking Page" and there will be a drop down menu near the bottom labeled "fare class." From there, you can opt to search for K fares or higher. Since U is available, it should return K fares as the least expensive eligible fare.

It's worth noting that systemwide upgrade certificates will not clear in advance on these routes (JFK-LAX/SFO), and will only give you priority on the gate upgrade list. You should make sure that the SWU is coded correctly to grant this priority.