Joined: Feb 2012
Posts: 19,381
Likes: 5,527
From: Rochester, NY
Bikes: Stewart S&S coupled sport tourer, Stewart Sunday light, Stewart Commuting, Stewart Touring, Co Motion Tandem, Stewart 3-Spd, Stewart Track, Fuji Finest, Mongoose Tomac ATB, GT Bravado ATB, JCP Folder, Stewart 650B ATB
"Please don’t suggest simply screwing on part B or somehow shaving the gear teeth of part B, as I don’t view those as adequately elegant solutions." xpacpal1x
Ok, I won't suggest the obvious and very functional solution. Maybe find a machine shop that can turn out a one off lock ring (would look much like a fixed cog's but RH threading). This suggested is some tongue in cheek...
I don't do hardly any web searches for question posters here but perhaps there's a single speed conversion kit that is made for the freehub body you have (a UG twist tooth version). The kit you got isn't made for what you have. Perhaps the company/people you got the wrong kit from have the right one? (Which I would be surprised if they did).
I see 3 choices and 1 hope- First is to use the thread on cog that you know works and costs nothing. Second is to get some custom part made. Third is to move on from this hub/wheel and get something that was intended to work as a single speed. The hope is that someone out there makes what you seek. Good luck finding that and I wouldn't hold my breath. Andy (who learned about square holes and round pegs quite a while ago)
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AndrewRStewart