Ya know, staring at that diagram something rather fundamental occurred to me: there's no benefit for all the TLs to move horizontally.
Think about it; at its largest diameter, the saucer is 2 decks high, tops. A stairwell will get me up or down a deck faster. And without lots of hallways blocked by TLs, I can also walk from one side to the other pretty quickly.
All the saucer needs is a few vertical-only TLs closer to the core, where the deck numbers are the greatest. As the decks get smaller, the need for TLs is reduced, so they would stagger as they do in a tall building. You would only need a single horizontal TL to zip down to the engineering hull.
After I had this realization, I dug out my FJ plans, curious what his solution was. Turns out, he came to pretty much the same conclusion. He does have a few horizontal tubes in the saucer, but they're relegated to runs to the EH, and a few key locations like the impulse engineering room and 'battle bridge'. Otherwise, he has a number of normal elevator tubes in specific locations to service vertical movement within the saucer.