So with a cable release, everything is fine, yes? That's a good sign. The shutter button pushes a lever that starts the whole game of firing the shutter and releasing the wind system so you can move to the next frame after the shutter fires, etc. A cable release simply pushes the same lever. Sounds as if the problem is with the shutter release button and its lock. The winding issue could be the button holding the lever in certain positions that, in turn, rotate the metering (film measuring system) ring to a partial engagement, hence the clunky semi-winding.
So I would guess the shutter lock is causing the problem. Often if a roll is going fine, you put the camera away, move around, and then the problem starts, it means the camera took a hit of some sort between the last use and problem. Maybe the lever got crunched and although it looks like it is in the 'release' setting, internally it is binding the button. See what happens if you play with the lock lever, moving it back and forth. AND check for any up/down motion. The basic idea is that as you rotate the lever it pushes a piece of metal out of the way or lets it drop back into a groove in the shutter button to lock. If the lever isn't engaging properly, the default is locked. Hard to say without seeing the camera but the lever could be loose.
There is a retaining collar around the shutter button. Put the lever in the locked position and see if this is loose. Use a small screwdriver in one of the slots to try to push it one way or another (use light pressure, not trying to undo a bolt or anything). If it is, tighten it. Or loosen it and remove the lever to see what is going on with its engagement with the stopping spring. That's really the most that can be done from the outside. And removing the front covers on an F opens up a big can of worms.
It can be fixed most likely and isn't just the 'new normal.'