issue with my distributor points on my 64 Dart

If you don't have a service manual wander over to MyMopar and download the closest one you can find there. You might have to settle for a year newer, or Plymouth vs Dodge, etc. Section 8 details testing shaft play. These girls always had some and "it is debatable" just what is too much. Best to observe on a scope or dwell meter, tips:

1....I never use a feeler gauge, I just set them "on the starter" with a dwell meter, then start it and recheck and diddle a bit from there
2...Make sure you have some good hi temp grease on the felt/ cam/ rubbing block, you want a tiny bit on the APPROACH side
3...If the books shows a dwell range, set to the SMALLEST number which is points further open, and therefore allows for "wear in."

4....If you are unaware, always set dwell first, timing last

5....A good condenser (capacitor) is required. The cap not only protects the points but also forms the spark. A vehicle with the cap removed will normally not start