hold the washer on the edge in a pair of vice grips then go slowly with your drill press. I've been wondering if your dist is the original 40+ year old unit & what shape the bushings (side play on the top slot assy) are in. I was thinking that maybe when they shortened the slots they exchanged the dist for a rebuilt one but maybe they didn't. See how much side play you have. Actually your lower end play is good from your descrip and they did no damage by deburring the welding and that was not what caused the excessive upper axial play, probably just a stackup of tolerances & now all is good only the upper play needs to be reduced to keep the rotor off of the cap terminals if the side play is good. But is the slot length they reduced it to correct for your app. But we need to solve the original complaint & worry about slot length later. As Scratchn said the rebuilt dists are a good deal for the money & you can even switch the cam/slots assy between the two as when they rebuild they only replace the 2 bushings and size them by reaming to fit the shaft as the rebuild dist will likely have the way too much mechanical (slot length) like yours originally had (36 at the crank ) before it was welded. I'd suggest get a washer under the nub, get a new cap/rotor and continue on to solve the original complaint unless your bushing side play is excessive right now. Save the old cap to drill it to check rotor phasing