What are the specs on side play of a headstock spindle of a Jet mini lathe?

I was spinning a bowl blank this evening, and couldn't get the tenon trued up. It looked fine while spinning, but then when I turned it over by hand, it was obviously not on center. I did this several times, and finally started checking things.

Since I had the blank on a worm screw in my Nova midi chuck, I checked to make sure the blank was tight against the jaws. Seemed to be - couldn't get it any tighter. Since it was seated all the way up, I checked to make sure the jaws were tight on the worm screw. I couldn't get them any tighter either. A back and forth side pull on the bowl blank revealed a "knocking" noise I couldn't pin down though. I took the blank off and the worm screw out, and thought it was the jaws clicking at first, so I took that chuck off and put another on. Same problem. REally curious (and aggravated) now, I took the chuck all the way off and checked the end play of the spindle. Not finding any play there, I pulled hard sideways on the threaded end of the spindle. Bingo! It made the clicking noise.

Now I was concerned. I loosened the belt tension, and checked again on the handwheel end. Yup. Definitely feeling motion in the spindle, I loosened the set screws in the hand wheel and tightened the hand wheel on the spindle as much as possible and re-tightened the set screws. A side pull still made the clicking noise. Durn!
I loosened the set screws in the hand wheel and the pulley and slid the spindle out. (yeah. it's that easy to change a belt!)

Close inspection revealed that the smaller bearing on the handwheel side had been "fretting" a little because the telltale rust marks were on the spindle and inner race. Still it doesn't seem that there's an appreciable amount of wear on the spindle. The bearing slides equally well on down the shaft as well as in the "wear" spot. The large bearing on the inboard end is tight on the spindle and will have to be pressed off if removed.

Subsequent measurements reveal the spindle to be about .001" smaller than the inside race of the bearing, and the bearing seems to be about .002" smaller than the hole in the headstock casting.

I don't have a dial indicator, so I can't tell you how much the side play is when it's all assembled, but I may check that tomorrow. I'll have to borrow the shops indicator and bring it home.

What are the allowable limits, and what should I do to fix this problem?