The CVN 65 isn't much bigger
You're confusing volume with length, or under-estimate the ship's funny shape. The saucer is only 120 meters in diameter, and then only at its thickest deck; the other 6 decks are between 10 and 40 meters in diameter at most.
The secondary hull is about 100 meters long, but is also only about 30 meters wide. And if we consider that the nacelles probably aren't habitable spaces, then the ship's internal volume would be relatively small.
Assume the ship's internal volume is something like 150,000 cubic meters. Assuming three-meter deck heights, that's 50,000 square meters or floor space, or 530,000 square feet. That's enough for a crew of 400 people to each occupy a compartment of about 1,000 square feet (about the size of a two-bedroom apartment) without having to share it with anyone else. If you then add in machinery, turboshafts, the engines, the phaser banks, the shield generators, the hangar deck, the impulse engines and however large the cargo bays are, you get a higher population density which is pretty consistent with what we see on screen.
So 400 people in a ship this size is just about right, IF they have really advanced technology, really good water recycling and very compact ways of storing their food.
On the other hand, the 750 meter Kelvinverse enterprise crams the entire crew into the saucer section and seems to give them a lot more living and recreational spaces, also includes larger laboratory complexes and probably more machinery for fabrication and equipment. The shuttlebay is enormous, as is the engineering complex. They end up having almost the same habitable volume as the smaller version, just with a shit ton of room for OTHER stuff that would have been useful for a ship on a five year mission.
so how can the TOS Enterprise not have room for 430 people?
Because a starship has to carry more than just people.