Can anyone explain why "I can’t leave it partially open or the radiator will fill with water and start spitting it out of the auto-bleed valve."? Why is partially open different from completely closed?
If the valve is closed, no steam enters the radiator, so no heat is produced, and no water is produced in the radiator.
If the valve is half-open, I guess the steam flows in fine (in reduced quantities), but the water does not flow back (looks like a design error in the radiator, or maybe it wasn't installed correctly; I guess that such radiators are fairly sensitive to being installed level)
With ever more water in the radiator, the water eventually exits through an overflow valve.