This is made all the easier when you notice that the set is sometimes differently decorated and equipped. Sometimes it has food slots, other times not so much. So I feel it's pretty well established that there are at least two or three different transporter rooms, even just from what we see on screen.
--Alex
I never thought of that as merely a food slot, but rather as a delivery station for whatever supplies might be needed for a landing party. Some transporter rooms have them, some don't. It is a mini-transporter - the delivery slot can beam in a phaser pistol from the armory, a communicator or tricorder from the quartermaster, or food for the transporter tech from the galley.
As for the number of decks and the thickness of the saucer, it very much depends on how you define "deck". Jefferies drew a cross section that had varying deck heights. Some spaces that are called "decks" might, in effect, be crawl spaces. Particularly towards the bottom of the saucer and towards the keel of the secondary hull, the spaces may be tiny but still be called "decks".
What can't be rationalized is an entire fleet of jetliners fitting in any conception of the hangar facilities. That is, unless the prescient writers of the series bible were thinking of drones. Might they have been confusing jet
fighters in a carrier hangar with jet
liners? Perhaps, and THAT is what I think is the idea they were trying to convey- a busy carrier hangar filled with fighters, recon planes, copters etc. Still beyond the limitations of the
Enterprise hangar and flight deck but more imaginable if many of this "fleet" are in fact workbee-sized utility craft.