The interest in the F-35C is understandable. Even with panic weight reduction measures in place, the F-35B cannot recover vertically, sea level, tropical day, with more than two 1,000 pound JDAMS and two AMRAAMs. That's the Key Performance Parameter and it is barely squeaking through as it is. So forget carrying Storm Shadow.
The F-35C also has much better range than the F-35B, since it has a honking big fuel tank where the F-35B keeps its lift fan.
Going cat/arrest also solves the AEW problem, since the USN is paying for Advanced Hawkeye.