The idea is not feasible.
Also your list of "carrier aircraft requirements" is incorrect, the JSF is a single engine aircraft, and landing gear is a major requirement of a carrier aircraft. The F22 is not a naval aircraft, was not designed to be, and never will be.
As produced, the F-22 is obviously not a naval aircraft. The tail hook is single-use, the landing gear is not reinforced, and the more modern stuff for carrier approach is probably not installed. All of that would be easy to change, and in fact a carrier version was proposed.
There is no such thing as "easy to change", you would have to redesign the aircraft from the ground up. You don't "navalize" an air force asset, you have the air force use Naval aircraft if you want dual use. The F22 is not and never will be a carrier aircraft.