@GeoPeg wow, that's some amazing detective work!!
First let me apologize. Pat (as usual) is right. Apparently only the Berk has a removable "bottom plate" that allows you to slide out the wheels and axles as an assembly. That's what I was thinking of. From your photos I'm disappointed to conclude that the Turbine didn't benefit from this design. So if you ever do need to change the wheels, gear, etc., you would have to pull and press them as with almost all Lionel trains.
Regarding your angular measurements... If I understand you correctly, you're saying that there's enough "slop" in the side rod holes, that the next tooth in the worm wheel will ALWAYS be picked up by the thread of the worm, before the outside of the wheel is pulled forward by the rod. This is an amazing discovery, because it pretty much busts my theory that different "timing" between the front & rear worm wheels is the reason why some of these locos run very well while others are noisy and balky. Maybe someday the true cause of the widespread variation in running quality will be found!
I'm not surprised at your 23-tooth count. There's a design philosophy that says if you want the mechanism to be long-wearing, use prime numbers for tooth counts so that over the life of the mechanism, wear is distributed evenly over the whole gear. In this case, it looks like it worked!
One more thing-- you don't necessarily have to pull the driver. Try wedging a slippery plastic "bread clip" between the wheel and the frame, or even inside the chassis between the worm wheel and the frame on the opposite side. (You can also use material from a plastic milk jug, etc. Cut it into a circular shape smaller than the driving wheel.) Among Berkshire owners this is known as the "bread clip mod." Do this as a temporary fix to see if it improves performance. And take comfort in knowing that If you do have to remove the wheel, you have at least 7 degrees of forgiveness when it comes to re-mounting it "in quarter." Great discussion here!!