I just went out and checked my distributor shaft today.
Mine has some play in/out also.
Maybe not quite 3mm, but pretty close to it.
So, you're not the only one that has some in/out play in your distributor.
My bike doesn't seem to be suffering any difficulties from it, but I have a Boyer Bransdon electronic ignition, and not points.
I don't think that is causing your problem.
Maybe somebody else can check their distributor shaft for in/out play, and tell us if they have any.
ace.cafe
I tallked to a Britsh bike parts supplier about Boyer electronic ignition. They sound terrific but the $2-300 makes me think it out a little. What do think of Boyer over others?
My Boyer is good when it's working right, but it's a little flaky, and occasionally gives some problems.
I'm not convinced that the Boyer is totally reliable.
Others have had problems too, and I believe that CMW quit carrying them.
To my way of thinking the other expensive electronic ignition by Power Arc is a better unit, and it has ability to switch to a retarded curve for hill-climbing or hard acceleration, which can save your piston.
So, when I dump this Boyer, I'm going with the Power Arc.
In fact, I already have it on my shelf, and am waiting for some of my other engine parts to be finished before I do a whole engine overhaul and install all my new parts.