The newer Vittoria ones have a third variation where the whole valve stem (including a fixed valve core) unscrews right from the bottom where it goes into the tyre. With these you need to buy new stem and valve combo's in the length you need.
It's a minefield out there!
That's my point, the "new" CX IIIs that I bought don't have completely removable valves like yours - the valve is well and truly fixed on the tub, but the valve core is removable. From a lot of searching online I discovered that my tub type is a very new change, but also the same as the original CX tubs, and the fully removable valve (like yours) was a change from the original that has now been reversed... I think...
Bottom line is it's not always clear :-).
Then remove the valve core, using the same extender as mentioned before attach it to the valve stem, (the other way around this time) and fit the core to the extender. As far as I can see, the same extender would work in both situations?
This seems like as good a place as any to moan about a pet gripe of mine. Manufacturers being inconsistent or ambiguous about lengths of valves and valve extenders! They never say whether the length includes the screw-down part of the valve (in the case of valves) and with extenders never say if the length is the total length of the extender or the length it extends by...