I know you have unwanted play in your spindle but I was just wondering if you had your work supported on the end with tail stock or rest. On mine I had to support anything sticking out of the chuck more that an inch or two if I was going to get any kind of decent finish. With the work supported it did a pretty good job with the tool dead center. I had the small insert set from Anytime Tools, also used HSS that I ground using Mikey' method. Without support there was little hope in a good finish. I know this won't help your spindle issue but it might help otherwise.
Jeff
Ahh, sorry, I misunderstood the operation of the bushings. Thought they were a two-piece affair with removable cap. I'll assume then that the slit in the bushing is lots wide enough to accommodate some wear in the shaft and still close up snugly. And if that's the case, I remain puzzled as to why they won't close down enough to eliminate the vertical play yet you are able to eliminate side to side play.
-frank