I do not think that there ever was meant to be, or will be a navy model. While the aircraft does have a tail hook, and it serves a similar purpose. The landing gear is just not strong enough to withstand the carrier landing. It would probably be a similar transformation that would have to take place like the YF-17 to F-18. Had to completely rework the landing gear and airframe to withstand the forces involved. The tail hook on the F-22 is for long field arresting gear at most military fields. Just wires strung across the far ends of the runway for a jet to catch before going off the end.
Actually, I saw an F-14 use this sytem at a local airport, at night, where it was at for an airshow. It used it for the main reason USAF jets have tail hooks; It lost the hydraulics for the brake system. It was completely dark out, but the F-14 pilot made a perfect landing, which was expected. It was cool seeing the sparks from the tail hook when it hit the runway. It was a nice slow deceleration, as you stated, not like what you would see on a carrier.
If a USAF aircraft tried landing on a carrier, besides the gear breaking, the tail hook would probably rip out of the aft fuselage as well.
Taking a Navy plane and making it a USAF aircraft isn't too difficult, though. Taking a USAF plane and making it a Navy plane creates huge problems. Besides all of the structural problems to meet the Cat/Trap criteria, the main landing gear would have to move aft, or have linkages to move the wheels aft (See YF-17 to F-18) the aircraft would have to fly the approach more slowly, the nose gear has to be twin wheel, etc. Of course, the main draw back to taking a Navy plane and making it a USAF plane, is it is now overweight for the mission.
BTW, I still think the best collection of flying doors is those as seen on the F-35B, which I think you've already modeled?
Nice F-22, btw.