Drive it over to Darlington, to Darlington Gun Works, and have Jim Kelly's nephew measure the wall thickness, and give you an opinion on whether or not it will be safe to hone the pits. If the barrel wall thickness is as you say he can likely clean it up for little cash outlay. And, you'll have an informed opinion on the overall soundness of the gun.

Congratulations on inheriting your G Grandfather's gun!

May God bless America and those who defend her.