HighUintas-
I just roughed out an undersized octagon. The barrel was 7/8” and I made the octagon, before heating, about 13/16” or a tad bigger. I heated it up until it was soft, then wearing welding gloves, gently pushed it onto the barrel until the octagon was formed to the flats. The octagon portion is about 1/4”-5/16” long and the rear part of the nose cap is maybe 5/64” thick.
The rear section was also formed with heat while on the barrel with a shim of wood the thickness of the web between the cap and barrel. A little heat and the sides were brought tight against the side flats. So, it’s shaped just like a metal cap, just bulkier.
For the final assembly onto the stock, I put a little epoxy under it in case there was a gap between the thin horn shell and the wood. I CAREFULLY added a copper rivet to be sure it stayed put.
You have to find the right horn. The one I used was pretty straight with a long solid section at the tip. I kept cutting the tip back to a point where the solid part was as wide or a bit wider than the rifle stock to allow for final shaping.
Sounds complicated but it really wasn’t. Hope this helps.
Good luck with yours.
Ted