Well, if they were to go down the route of crewless frigates, then they'll have enough spare crew for the carriers.. DARPA are already planning such ships - see
US crewless, automated ghost-frigate project takes shape ? The Register
Of course the ideas not new - see this german test from 1928
Image of crewless warship in mock battle - august-1928 by Science & Society Picture Library
Now if we were to give up on the F-35, maybe buy a few second hand F-18s as a stopgap and instead go for unmanned fighters then the manpower situation would be even better. By the time the carriers will supposedly be fully capable in 2030 with a full air wing, then the F-35 will be superceded technology anyway: everything will be UAV. Time to make the jump NOW