Just noticed on the
Star Trek Blueprint Database, that
Jim Botaitis revised his Enterprise deck plans to include a bridge concept that pulls the bridge forward from the centerline under the dome about 6 feet. This change puts the bridge in the "facing forward" orientation
and leaves room for the turbolift to slide to the rear and enter the nub/turbolift feature (almost).
https://www.cygnus-x1.net/links/lcars/blueprints/tos-enterprise-deckplans/1.jpg
JB sketched this for the Deck 1: "Original" Bridge, but I can see that it could apply for the Regular Series bridge (in the 947 ft. hull to boot) by sinking the bridge down about 4 feet. Getting the turbolift car into the nub tube is still a problem, but if the car drops down a little first, then slides into the tube, it might work. I even included a second vertical turbolift shaft to help with congestion.
My conceptional adaption to JB's plan:
The nub extension of the tube above the turbolift car could be for emergency ejection of the cars as lifeboats, or just a work space.