Thomas,
I don't know why you're posting this link, but working on the assumption that you want to know a bit more about the issue (as opposed to just throwing up carrier related 'bad news' ), here goes...
There was no requirement for all of the F-35 support equipment, spares, etc. to be transportable by COD, or V-22 for that matter. There was a requirement for the F135 engine to be capable of being moved from ship to ship by wire RAS in its container. Incidentally, the F135 is Government Furnished Equipment (GFE), so responsibility for sorting out how it gets on a ship lies with the US DoD and in the case of the RN, the MoD. LM's main task was was working out how to change an F135 while the ship was moving about - and that was quite a challenge.
The USMC already, some time back, demonstrated a concept for moving the power module of the F135 (the core of the engine) around in a V-22, using a specially developed 'sled' to reduce overall size. The complete F135 is a very large piece of kit, and is normally (as far as I know) moved around in its sections (or 'modules'). The UK operated for some years with Sea Harriers and their Pegasus engines, which could only be brought on board by crane alongside, or possibly by (very) short range vertical replenishment as an underslung load. (We once moved a Peggie from the ship to ashore in Bermuda using a Sea King).
So, my take would be that spare engine modules (or even complete engines) would normally be brought on board ship by crane whilst alongside, before the ship sailed, or at designated ports during deployment - just like any other large items of stores required during a deployment. Modules would be assembled into complete engines on board in the designated bay near the hangar. Next step along would be via ship to ship RAS, and if that failed, perhaps using a friendly local USMC V-22. Or perhaps they could embark a Chinook for those occasional 'big lift' jobs - the RAF have plenty of them, and the ship has a bit of space. Perhaps the RAF would be able to provide a continuously embarked flight of, say, three aircraft for those unforeseen arisings (humanitarian work, lift and shift, rescue work, disaster relief, etc.).
Hope this helps. Best regards as ever to all those superbly professional types who handle maritime logistics,
Engines