I think I remember seeing your musket (it was pretty well made) on a porch railing when you first finished it up but I cannot remember the time period from which it dates?
I think to generate the best ideas maybe we should consider time/location?
Really about anything 'could' be believable, anything from a case skinned rabbit, to a flour bag, to a British cartridge box would have accompanied a Trade musket.
If it was me I would make a small bag of period correct material- big enough to hold 3-5 paper cartridges a tommy bar/turn screw for the cock, a feather, and a spare flint. You know enough to live in the bush happy, fed and defended for a couple months.