The agitator really isn't supposed to be stationary or slow as compared to the spin - at least not in more recent machines - as this would negate the usefulness of the agitator mounted softener dispensers. These take for granted that the agitator is going to spin fast enough, and consistently so, to fling the softener solution to the outside of the dispenser wall and hold it there until the machine stops for rinse fill.
Usually clothes will take the agitator for a ride for a while until the basket accelerates enough that clothes are pressed to the sides and are no longer touching the agitator. What I've seen is that when there isn't enough 'grip' between the t-bearing and the spin tube, OR the other components between the spin tube and the agitator shaft, the shaft will not spin at tub speeds, and the agitator then slows down, or rotates intermittently.
When I quit putting grease on the surface of the t-bearing, my issues with this stopped, at least the issues that I was creating. From that point on, I have left the collar of the t-bearing as dry as possible. When the centerpost leaks, oily, detergent and softener laden water will coat this area and make it at least temporarily slick.
Mark - there is a significant difference between your 1960 WP and Chris' 1981. The centerpost is 5 inches shorter in the '81. Unresealed machines eventually loose their centerpost seal through use and wear, and water much more readily will escape under the 81's agitator. Your machine, having been re-done and re-sealed by you not that long ago, probably does not have that problem yet.
The rub though in all this is that when the agitator doesn't spin fast enough or at all, it wears the seal(s) even faster than if they were all traveling at the same speed, thereby hastening the wear even more.
I believe conditions internal to the transmission can cause some resistance on the agitator shaft as well, but not in a healthy transmission.
Gordon