Are you sure that your not getting drips?
If you're getting drips that fast while at rest, then spinning should yield much higher rate. Are you sure that your just not flinging the drops all over the engine compartment?
Do this experiment:
Adjust the drip rate to the few drips a minute when not spinning the shaft. Make sure that you do this with the locking nut tight. Go for a ride with the motor running while having someone else drive. Go below and put a piece of Cardboard round the stuffing box, but about 5 or so inches away. See if the cardboard gets wet, if it does, then you're just flinging the water off instead of dripping, which is why you don't see it drip. Also, is the front of the packing nut wet, by front I mean where the shaft enters the nut from the motor side. If so, the water is getting to the shaft and cooling
When locking the locking nut, it is very easy to think that you are not moving the nut, when in reality your moving it also.
If you liked my advice/response, give me some rep points. If you didn't......well what do you expect, it was free.