We could argue that the maximum number of shuttles stowable aboard a
Constitution is much higher than the number of shuttles
operable from such a vessel. Sure, you could jam-pack the upper hangar deck with six shuttles, as in TAS "Mudd's Passion", but you'd get fender-benders trying to maneuver one of them out. (You might google for pics of "aircraft transports", old escort carriers with their flight decks packed so full of aircraft that they can get off with the help of a crane only. A viable way of transporting those planes, but not of operating them.)
OTOH, the lower hangar deck must have further spaces, since at least one shuttle in TOS, and possibly three, must be stowed there when we see just a single shuttle depart from the upper level. But the lift between the two levels cannot accommodate anything larger than the TOS shuttle, assuming the lift and the turntable are one and the same. (It could be that there are larger lifts at the forward end of the bay, behind twin rolling doors similar to those we see in the ST5:TFF shuttlebay.)
At least two of the TAS shuttle types are far to large to be taken "below decks", and essentially hog the entire bay for themselves when carried: the aquashuttle from "Ambergris Element" and the long range shuttle from "Slaver Weapon". Still, both carry registries that indicate them to be auxiliary craft to NCC-1701, not just something Kirk loaned from the nearest starbase for the duration of a mission. But we could always say that Kirk did exactly that, and his deckhands then were swift at stenciling in new registries.
I'd argue that a
Constitution's shuttle complement would be mission-dependent, and that Kirk offloaded most of his other shuttles for "Ambergris Element" and had a particularly busy day in "Mudd's Passion". One of the craft seen in the latter episode looks a lot like Carter Winston's private yacht from "Survivor", and it might be that Kirk was still hauling that piece of junk at the time but ditched it at earliest convenience.
As for the TOS numbering scheme, it could be more or less arbitrary, but consider this: the
Galileo was #7, the unseen
Copernicus supposedly was #3, while G and C are the 7th and 3rd letters of the alphabet, respectively... It could be the names are given to match the number, but it could also be vice versa, explaining #7 for the fourth shuttle out of four.
FWIW, the
Copernicus from "Slaver Weapon" is #10, the aquashuttle is #12 (in most shots anyway; others have it as #7), and Mudd's shuttle is #12 as well. The originally unseen
Columbus from TOS "Galileo Seven" was rendered as #2 in the remastered and re-effected version of that episode.
Timo Saloniemi