What’s wrong with the F-22? Mod that thing for Navy purposes! Carrier landings? I don’t know!
One of the reasons that the F-35 is so expensive is what happens at take-off & landing is different for all 3 versions of the plane. Even just making a plane that is intended to be capable of catapult take-offs & arrested landing (ie. a navalized version) makes the plane considerably heavier than a plane designed to operate from land. The weight penalty alone impacts performance significantly.
Google the fly-off between the F-15 Eagle and the F-14 Tomcat that was put on for the Shah of Iran. Fascinating reading.