Jim,
I have been fortuned enough to be able to look at chambers of the original Sharps and the Hepburns. I also have two chamber casts one .44-77 and the other was from a Hepburn that was actually used for the creedmoor matches complete with loading tools cases and patched bullets. This fellow asked me if I had some bullets and I said yes. I asked him if he could make a chamber cast because I would like to make a reamer of an original Remington Straight. I sent the cast to PT&G and Dave measured and sent me the specks. I had him make some changes on the neck diameter because it was closer to the .45 caliber than the .44's now used and the chamber end transition was a 4º funnel from the chamber wall to the lands.
All of the Sharps I have an opportunity to bore scope the transition had a funnel type taper and what looked like a very shallow groove.
I since have several reamers made for the rifles I have with the funnel transition from 4º to 7º.
Below is a .44-77 Sharps cast and this chamber and bore was rough but if you enlarge the photo you can see a very shallow transition. As near as I can measure it's a 3º very shallow. The cast on the carpet is a Remington straight cast.
I have added more reamers since I took this picture
I like to call this type of chamber a lead bullet chamber
But in all reality the new modern 45º transition what I call a chambered wall, this type of chamber transition also works, but I give the funnel transition the leading edge over the wall.
Kurt