This is "seat of the pants" thinking, but it seems to me that horizontal movement, if it is only evident when one applies considerable force in the horizontal plane, is not a deal killer. If the tonearm is loose and flopping left to right or etc in the horizontal plane, that is a problem. In my case, the tonearm can be rotated in the horizontal plane but only with considerable effort, and it never moves during actual use, where the drag on the pivot is only in the milligram range, so I decided to forego the repair process, for the time being at least.
Colby Lamb offered to make me a new set screw with a widened "head" such that it tightly occupies the vertical channel in the B60 shaft and thereby prevents wiggle. But he needs the whole part in order to do the job accurately. I don't want to send it to Oregon just now. Thanks to Nandric et al for the alternative cure mentioned above; maybe I will try that since it takes only a few minutes and can be done at my home, 2700 miles from Oregon. After I screw up the screw (or lose it in the carpet or under my work bench), THEN I will have to send it to Colby.