No doubt in all your investigation, you have learned that precise shifter adjustment is critical with these hubs, as is free and unfettered movement of the shift cable in the housing. Issues with either of these can cause the problems you describe.
Also, in lubricating the internals with regular lithium grease, you have introduced another problem. The internals need to be lubricated with a semi fluid low viscosity grease, or better yet, with oil.
The reason for this ties in with the necessity for accurate adjustment. In gears 2,3,4 and 6,7,8, shift pawls rise from the axle to couple sun gears to the axle. If the grease lubricating the actuating arm and the pawls is too stiff, it can prevent the pawl from fully extending and completely engaging the ratchets on the inner circumference of the sun gear, which is also what happens when the shifter is slightly out of adjustment. Incomplete pawl engagement will result in skipping.
So, if there is heavy grease in the actuating arm and shift pawls, I would wash it out with solvent and give it a oil dunk lube job, (I've done it successfully with ATF) lube the outer bearings with wheel bearing grease, ensure proper shift cable adjustment, and ride.
Before too many seasons pass, you will have to dig in a bit further to clean and lube the drive side cone, but that's another discussion.