John McGaw
Difficult one. The South Union Shaker Museum in Kentucky had, IIRC, authentic Shaker-ish broom-making equipment on display and would probably allow a close examination on request for serious historical research. Ditto, Berea College has a live working shop making just what you describe and they might be willing to allow examination. I've never seen plans anywhere but, of course, I've never done the digging it might require.