The shallow taper of the original Hornet shoulder might as well be no taper at all. You cannot headspace off it, because the primer blast will drive the case forward to the limit of the rim recess anyway.
I have a T/C barrel that wouldn't headspace properly on my Gen 1 receiver, maybe because the receiver is stretched a few thou, or maybe it's just the tolerance stack. A .006 feeler would fit behind the case head with the action closed. Brass life was bad. A case that survived the 2nd firing was a surprise.
Reaming it to the "K" solved that problem completely. While it's still not a 1MOA tackdriver, it puts 'em all on a woodchuck's torso at 100 yards if I get a good rest, and all my remaining brass has survived half a dozen firings. I don't load 'em extremely hot, (30k psi or so), so I can use pistol primers. Best bullet is the Barnes 36 grain Varmint Grenade, best powder by far is Lil'Gun.
My Stevens 44 1/2 is also a "K". It is still waiting for me to finish stocking it, so no performance report. As far as I'm concerned, any other Hornet that falls into my hand will feel the bite of my reamer.