Here's a more lazy suggestion:
Whilst I fully agree with the advice about wax, for such an early rifle the semi-gloss finish it has right now doesn't seem like a major crime.
And the wood grain really looks nice. The glint of the camera may be making it appear glossier than it is - the finish in the last picture in your series [showing the fore stock] looks absolutely spot-on to me.
So... you could try rubbing it and buffing it with beeswax [or another microcrystalline wax] to get a finish approaching the effect 22SqnRAE describes, but without doing any of the stripping... anyway, that's what I'd do first of all...