Back to the Constitution-class hangar bay for a moment: the freeze-frame "King Daniel" gave us of the wireframe visual of the hangar seems to confirm your thinking re: that class having on average 24 shuttles...
Yeah, I had originally based it on the view from the shuttlebay in the 2013 videogame, which showed landing pads sufficient for 16 shuttlecraft; the same bay had 4 unused landing pads next to the clamshell doors with room for 4 additional shuttles, plus some elevator-like structures leading to what I assumed was a hangar below decks (probably Shuttle Bay 2 that launched Mudd's ship in STID). That would make for 24 shuttles maximum.
The video King Daniel linked to shows a reconfigured bay somewhere longer than the game depiction and knocks out the decking between the main hangar and the lower level. So the shuttles here are in four rows of six (port, starboard, upper, lower) instead of four rows of four, making 24 in the main hangar alone. The lower level is now a cargo bay, but obviously has a large exit hatch for visiting spacecraft and/or short range shuttles that shouldn't need to use the big door.