This is the sign of a worn impeller stop in the head. Years of running with nil to none lubrication have worn the center portion of the bridge and now allow excessive forward-back movement of the impeller shaft.
Solutions include buying the "long" shaft (they come in two overall lengths) and pressing the impeller on doing a sort of "trial fit" with component parts of the pump as guide (pin the impeller when you find your spot)
OR building up the end of the impeller shaft with weld and grinding flat.
OR similarly tapping the end of the shaft and screwing in a brass bolt - and then grinding down similarly.
OR drilling & tapping the head bridge to install a brass hex bolt to act as "seat" - some machining of either the bolt or the pump shaft may be required to get the proper lateral shaft motion.
Your target is 0.005 to 0.010 free motion, this being thought optimal by those who do this for either a lip seal (LIFETIME sealed pump) or the original packing seal.
Generally, pulleys as found are fine with "B" section belts. Some metric belts are now being sold by the vendors which are at best "variable" in how they meet the pulley grooves.
A Gates B43 belt may be the best. I had some problems with this but Joe at Tam's Auto Parts had some suggestions when I told him my model year, pulleys, how much free play I was seeing. I'm running a Tam belt of unknown source marked "42-6324" currently.
Good luck. It sounds like you're bringing this one back?
Joe K