tested the direction with the lock ring
By turning it in the opposite direction?
Um, I assumed that the sprocket is threaded the same way as the lock ring, as they seem to be on the same thread on the hub.
Is that an error?
Opposite way. Otherwise the lockring wouldn't be holding the cog on.
The cog comes off anti clockwise. Ie the opposite to the way the chain would be pulling it if you were pedalling
Yeah, they are both threaded the opposite way. If you look closely they have their own threads. That should solve your problem.
@ChasnotRobert started
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By turning it in the opposite direction?