I would not use grease or oil in the packing gland of the stuffing box. It is designed to be lubricated by water, not grease or oil. This is why a few drips of water while the shaft is in motion is normal - water is lubricating AND cooling the joint.
I once made the mistake of putting some oil in my stuffing box. The old packing quickly decomposed and we had a bigger problem - a fast leak at the rear end, after a period of inattention the cabin sole (floor) had 6" of water above it. The laws of 'unintended consequences' come into play when you mix stuff that is not supposed to be there with stuff that is. The residual flax packing material thoroughly gave up the the ghost with the addition of hydrocarbons (oil) and sea water.
With all due respect to Capt. Boasun the best authority and tutorial on stuffing boxes on the net is: Re-Packing A Traditional Stuffing Box Photo Gallery by Compass Marine at pbase.com
Personally, I do not believe that the noise you are hearing is from the stuffing box. I will bet even money that your tranny needs a slight adjustment. I have to shift slightly into the range of Reverse to get the prop to stop spinning altogether and then there is a slight whine as Reverse is partially engaged. If I do not back off towards Reverse the prop keeps spinning slowly in forward and there is no whine. There is no 'click' to define neutral on our boat and knowing when the prop is not spinning is a bit of an art more then a science.
I respect all the other suggestions here in that:
- engine/shaft alignment
- cutlass bearing
are all possible culprits.
I will add one more possible problem: barnacles or growth. Is your prop clean?
I am not an expert in A4 transmissions (yet) so I refer you to: Moyer Marine Atomic 4 Community - Powered by vBulletin
for further guidance.
Good luck and enjoy the whine.