A brad is a small nail used for wood, I think what you need is a brass rivet. This link might get you started;
https://www.microfasteners.com/brass.html
The broken piece should fall out with a few gentle taps using a pin punch. Fellows who build model steam railroad engines and things use these rivets, maybe you could find someone local who could make quick work of the repair, there are clubs around. Just a thought, good luck!