I can see a long bolt sticking out of the headstock casting and the only other screw in your last picture looks to be a coarse threaded grubscrew partly unscrewed from the small sheave on the pulley.
All three pulley sheaves and the (middle) gear in your picture should be mechanically joined to each other and be capable of rotating freely in the spindle (to drive the backgear).
Is the bull wheel the only thing solidly keyed/joined/fixed to the headstock spindle?
The smallest gear in your picture I assume drives the screwcutting gearing so somehow that must be part of or fixed/keyed to the spindle.
What kind of bearings does the spindle run in?
Can you show a picture of the end view of the headstock that shows that end of the spindle
Ian P