There is a lot of information on the axial clearance on the oil pump gears. However, I have found none on the radial shaft clearance ("side-to-side"). Nothing in the Chassis Service Manual. Reason I am asking is because I can clearly feel the shaft moving side to side, even now when oiled. Considering how bushings this size usually are setup, I see no reason why this shaft should have more than 0.001"-0015" radial play? Seems like a tricky machining operation to drill the passage out and install bushings. I suppose running a reamer in reverse like some people do with throttle shaft bushings might be an idea but.... A bit disappointed Buick didn't put bushings in it. Guess I am reaching out as a last resort for input before ordering a timing chain covers.
I would think too much slop or play would result in wear all down the line, gears, oil pump pocket & cover. Set clearances tight on pump cover and that unwanted shaft play will allow gear to score cover surface.
How much play are we talking about? A sheet of note book paper is like .004”, can you rap a strip of that around the shaft and get it to drop into the pump?
Off the cuff, I wouldnt expect more than .002-.004 - maybe toward the latter given the disparate heat expansion rates of steel and aluminum.