Watch runs well dial side up, but not dial side down

[dadistic]

Ok, here is my take. The screw fixing the stud in place is missing, which has allowed the stud to move out of place, causing problems. The most like reason the stud won't come out is that the screw was tightened enough to raise a burr on the stud, which is catching as you try to move it out.

As you said, it will require a bit of a tap to get it out, and then the burr will need to be addressed and a new screw put in place.

Have Fun!