The distributor shaft play was a some what common problem on high mileage 6 engines in the sixties GM service school taught you to install two bushing in distributor instead of the one as original. There was room for two in the housing and on the shaft. This solved a high speed miss problem. If this is a really serious problem at higher RPMs you may have a broken valve spring that has enough tension to close valve at idle but not when rpms increase.
Big Bill

Been there, Done that, Hope to live long enough to do it again.
Big Bill
I.I.# 4698