Interesting solutions I'm a tool and die maker and offer this idea based on tool room experience. Could the frame be mounted in a mill then with a boring head the OD is cleaned up then a bushing/sleeve made to fit over the stud or press fit in the hammer?
Two great sources for Bullseye shooting information are John Dryers site and the bullseye-l forum.
This time of year clubs with a indoor range may have a bullseye league. Show up at a match to observe and ask questions, before you know it you'll have several people offering advice about...