The CVN has a hell of a lot more volume than the ENT-TOS. When you get down to it, a lot of decks are in the neck. And the livable space consists of a saucer and cylinder that take up only 2/3 or so of the length.
Then you have 7-ft wide corridors everywhere, so slash your space by about 1/3. If you want any of the ship's space to be taken up by things other than living quarters, having any singles (as per canon) doesn't make sense. I've done a few versions of this myself, using the 1080 ft ship. I could fit maybe 280 people into deck 6 if I went 4 to a room. That's subtracting space for impulse drives, labs, computer components, those damn corridors, and turbolifts. And jefferies tubes. And so forth.
I personally like to stay as far away from the FJ BPs as possible, since the ship ends up looking more like a passenger liner than anything else.
Anyhoo, that's my 2c.
EDIT: I was tired last night. Fixed my typing flubs.