I want to mount my pencil air-powered diegrinder on my lathe's cross-slide so I can true up the jaws of my chuck, along the lines of this article (at the bottom of the page).

The tricky bit will be getting the grinding wheel shaft parallel to the bed so that the jaws end up ground parallel... The cross-slide on my lathe is mounted on an ungraduated swivel and I have yet to find an accurate way to lock it so the slide travel is perpendicular to the bed...

The best solution I have come up with to get the slide perpendicular to the bed is to put the DTI on the cross-slide and the plunger on one edge of the chuck face, then spin the chuck to find the min and max values and rotate to set it midway, then keeping the chuck stationary, traverse across the face of the chuck and adjust the slide swivel to get the same reading and keep traversing back and forth and adjusting until it is constant across the face. That gets the slide right, but then how do I get the die grinder shaft parallel to the bed. Its not long enough to DTI sensibly along the shaft over the travel of the saddle.

Suggestions?