Thanks Jim, your comment about the grub screws was right on. I loosened both with a 1.5 mm hex key enough that I could remove the knob and collar with the screws altogether. The attached picture shows the result. The brass shaft slides in and out freely. So as far as I can tell the only thing that determines the axial "slop" is how that collar is situated. There's quite a bit of grease and a washer on the backside of the rear cell around where the shaft goes in.
So my fix was to pull the shaft out as much as I could, slide the knob back over and press it into the back of the rear cell while tightening the grub screws. This seems to have fixed the problem, or at least 99% percent of it.
Now for a new question. I've mounted the scope on a Vixen Porta mount. This works great, except that dovetail is on the right side (looking from the eyepiece) instead of the bottom. This puts the focuser at 12 o'clock, above the eyepiece, and the finder down at 7 o'clock, which is awkward, especially when looking near the zenith.
One (possibly bad) idea is to remove and rotate the rear cell 120 degrees clockwise. This would put the focuser and finder in much more convenient locations. My fear is that it would also mess up the collimation, and that I'd botch up what is at the moment a nice telescope. Thoughts?