They shouldn't have any noticeable play. Back in the day rebuild kits were offered, but I haven't seen that in a long time. A 1112403 Delco fits 1952-62. There are lots of them around, but if they weren't lubricated they will be in the same shape as yours. I just wiggled them. If they had slop, I threw them away. But I am almost 83 years old and don't do things very scientific. There are lots of after market distributors for sale at various vendors. I would think the electronic pickup would be more sensitive than points.