I also think that it might make a lot of sense to put that piece into the Syndication Links plugin as well since that’s a piece that directly relates to something Brid.gy is looking for to do backfeed. Doing this may also make even more sense if Syndication Links becomes a tool for POSSE as well. It would be nice to have a definitive one-stop-shop for syndication and backfeed related functionality.
As a “throw-away” aside, if you’re looking for a good name for such a thing, perhaps Boomerang? Throw your content out there and all the responses return back to your site?
The basic functionality of Bridgy Publish is in Syndication Links now. Not the registration piece though, but it is a much cleaner implementation, though currently more basic.