I ran across an old article regarding dowling irons at the tip to cut down on vibration. I thought it would interesting for builders. Steel shafts only. No idea if the reference articles was for .355, or .370. But fluted dowels come in different OD.

“5/16″ dowels 1.5″ long(make sure to drill a hole down the center if you’re installing them and cutting them for air to escape. I install mine after the heads are on, some do before.  To save drilling, buy hardwood fluted dowels. They’ve got flutes running the length of the dowel and don’t need to be drilled down the center. You can install them prior to shafting too, but I like doing it after because if you don’t, you end up having to drill the center holes out twice because the epoxy dries and creates an air pocket between the dowel and shaft tip and you’ll never get the heads seated if you don’t”

Old school methodology, but certainly works well. Fluted dowels can be found at most larger hardware stores.

Answered question