Well if you have a flat top burning through engines my guess is by 4-5 in a rapid succession the Navy would be loading up an Osprey. Again the other method by supply ship will take a lot longer to meet up with the carrier. Although they can load more in one go.
Given the reliability of modern engines, and the diagnostics available to detect issues before they happen, you do have to wonder whether the engine replacement issue isn't a little over egged. Carriers will have plenty of storage space, and the reduction in air wing types means the number of types of engines needed to be carried is dramatically lower than it used to be. QE for example will only require 2 types, RTM322's for the Merlins and F-135 for the F-35's. A USN carrier will need 4 at the moment. Although they're costly, you'd think keeping a few spares onboard is a damn sight cheaper than developing, purchasing and maintaining a COD capability if that was the main goal.
One interesting thing is the UK has developed the Rolls-Royce Heavy RAS system that will be fitted on the FSS ships that will support the QE Class, it's a lot faster than normal RAS and can handle far heavier loads, up to 5 tonnes, one of the specified loads was a F-135 engine in its transport case....I've no view on if that is safer or easier than a sling load under a Merlin though. It should allow the RN to shift 600 tonnes of stores in 5 hours, which is some going..
The HRAS training rig at HMS Raleigh can be seen here...
