After much looking and thinking, I found the reason why the 4th axis table was moving in an unsteady, jerky fashion. It was not mechanical.
I took off the servo motor and when directed to rotate steadily, it would, instead, accelerate and slow down four times over a complete rotation, which was kind of severe and led to quite a bit of vibration.
It was narrowed down as a resolver issue, since the slow downs were at each 90 degree position and also because the table moved exactly 360- degrees when instructed to do so.
Long story short, it turns out that the voltage to the resolver primary was too high, which at times caused bad reading of the sine and cosine outputs of the resolver. I lowered it and the motor turns smoothly. I discovered this because I INCREASED the voltage at first and that made a bad problem MUCH worse -- but it told me where to go, that I had to go the opposite way.
I reassembled the rotary table and put "Pennzoil marine grease" into the place where rotation of the servo motor is turned 90 degrees. The "brown grease" that I took out, as I realized in the morning, was Shell Alvania. I should have used the same thing but I did not think about it. I think that for the amount of use that this RT will see, Pennzoil marine grease will be just fine.
This is a place where the servo motor's rotation is turned 90 degrees, and also reduced by some good factor, with a pair of 45 degree gears.
I packed about 80% of the volume with grease and left 20% empty.i