By your description below I believe you have a secondary ignition misfire. Here's some things to look for.
Top photo, in 1972GY8SE's post, is the inside of the distributor cap. He's telling you to look at it.Ok that sounds like it but where?
When it moves slightly is it a small but rapid movement?Moves slightly .
.012" play is not that bad, a spinning shaft tends to run on center. There is no real load on the shaft, anyways.View attachment 760223 The play is 0.012 inch it means that the pickup gap of 0.008 vill not be konstant the rotor vill hit the pickup is this the problem ?!