Well, I'm bringing this one back from the dead. Curiously enough I'm in the same boat as the OP. I happen to have the same bottom bracket that I bought years ago. Anyway, I have some questions for the well informed.
1) Campy changed it's taper in 1994 so pre and post 94' aren't compatible (also the bottom bracket length went from 109mm to 111mm) While this White Industries spindle may have a Campy taper is it likely to be pre-94'? (Didn't White Industries make these BB's in the late 90's?)
2) This is more directed at the OP, but, my spindle is 111mm (I pressume yours is as well) The cups on the White Industry BB are relatively thick, so while you have the ability to "float" the spindle to the left or right there really isn't much room to actually move it. Were you able to get a *perfect* chainline?
This is probably more hassle than it's worth but I thought it was worth a shot. Anybody have a 68-P-120 Bottom Bracket?!