I don’t know much about Parker factory choke profiles but several Parkers I owned and measured had tapered chokes right out to the muzzle, similar to A H Fox guns. Fox used a full taper choke profile during the Philadelphia era and that carried over to about the mid-point of Utica/Fox production. The Fox choking was done from the breech end and the tapered reamer was run in farther toward the muzzle to make increasingly more open chokes: X-Full --> Full --> Modified --> Imp Cyl. Even the “Fox Cylinder” choke had a few thou of tapered constriction depending on the gauge. The same thing could be done from the muzzle using a reverse-tapered "draw reamer" but it's far more complicated and would require a rigid lathe setup or similar.
Just for info, here’s a tapered reamer I made for 12-gauge to open chokes from the breech end and have it
absolutely concentric with the bore. It was an expensive setup with the custom made reamer that matches the nominal Fox taper along with a set of bronze centering bushings at .003” increments, starting at .724” diameter for real early Fox guns, and ending at .748” diameter for use in the largest bore Super-Fox guns. The drive rod was made from TG&P steel shafting. Works like a champ and the newly cut choke(s) will essentially duplicate Fox factory work.
JFI, I made this up for my own use and am not "in the business". One of these days I’ll get the same setup made up for 20-gauge and maybe for 16. Generally I'm an advocate of leaving factory chokes as made but there are times to open them - and then I want the choke to be tapered and without a straight/parallel section at the muzzle as done with adjustable reamers, just my preference. Personally I don't test shoot the gun for pattern % while doing this work; I did that first off quite a bit but determined to my own satisfaction there's a very good correlation factor between bore and exit diameter at the muzzle, and pattern %.
The back end of the reamer has a 1/2" long straight section and then the taper begins. Reamer was just used yesterday and isn't cleaned as yet, some small cuttings in the flutes.
Plenty of length to use in 32" or even longer barrels and still clear the barrel extension.
The drive end is square for a large tap handle
