I can't help you with the Herret question, but I can give you a little information about your Bee. For a time in the early 1970s TC made some of these somewhat tapered round barrels. Most of them were "scope only" models and had no sights. The only ones I've ever personally seen were ribbed hotshot barrels with internal chokes, and they were not very much tapered, but some. I'm surprised to hear that they made some with soldered on front sights, but I guess yours is proof. The round headed screw was used with the early forearms, which had a spring loaded ball or plunger that snapped on to (over) the round head. Unless you can find one of those at a gun show or something, you'll either have to use the standard bull forearm or get yourself an octagon forearm and fit it to your barrel by removing wood. A dowell with sandpaper wrapped around it should do this job fairly easily. Then seal the inside with some stock finish.
Hope this helps.
RonF