The spindle mounted pulley set is free running on the spindle on an S7, not keyed – it runs on bronze bushes & there is an oil nipple in the pulley. Drive to the spindle comes from a Woodruff key in the bull gear, the bull gear being connected to the pulley cluster with the retractable half round dog that is mounted on the bull gear.
The Woodruff key is small IIRC – the parts list says it is a "No. 404" key – so there is a possibility that the key has been sheared trying to remove the chuck.
A 'pdf of the Super 7 manual is easily found with a quick Google. This includes the exploded parts diagrams at the back. Worthwhile downloading a copy for reference purposes.
I don't think it is recommended to remove chucks using the chuck key inserted in a pinion, as this can split the square end of the pinion or dmamage the pinion bore.
Nigel B.