I think I would have that barrel freshed out. I don’t know what those gouges are in the bore, but they don’t look good.
Sixty grains sounds like an adequate load to me. If the rifle is one of the brass-mounted, mass-produced Hawkens, I don’t think the grooves would have been very deep to start with. A lot of fellows will tell you a 1-48” twist is a “compromise,” and some will tell you it is too fast for patched round balls, but that isn’t necessarily true. The depth and configuration of the grooves makes a tremendous difference. Anyway, if the rifling in your gun is badly worn, the heavier powder charge may be pushing the ball too hard, so It doesn’t engage the grooves adequately so it skates across the lands. There are other possible causes of reduced accuracy with the heavier load, but I think this is one to consider. If the rifle shoots well with 60 grains, that’s what I would shoot.
However, I really think the best option is to get the bore recut. If the barrel is 15/16” across the flats, you could probably have Mr. Hoyt bore it out up to .54 caliber. I have a T/C Hawken barrel in his shop right now, from an abused and neglected rifle I bought used. He will fresh it out to .52 caliber (balls and moulds are obtainable), keeping the same number and configuration of grooves and pitch or twist, but cutting the tops of the lands to .520” to smooth them up, and the grooves to .011” (his recommendation) for patched round balls. Non-standard calibers are nothing to be afraid of in muzzleloading.
Good luck with it! We hope you’ll keep us updated on your progress. It would be great to get your dad’s rifle fixed up and out in the field again. He would probably be pleased.
Notchy Bob