IVe cleaned the gun if the field a few times.  Good enough for a few days.  A few wet patches, a dry patch or two, a little wd-40 patch then a dry patch.
Get a spare breech and put it in.  Perfectly clean, no fouling shot needed.
Windex, moose milk, 20:1 water/ballistol, or just water for the wet patch.
Done that with stainless barrels and regular steel flintlock barrels too.  I use goex 3f black powder, so I am more corrosive.  triple seven and pyrodex is not totally clean.  It's a bit different enough to prevent fire and legal issues with traditional black powder vs regular gunpowder..
I know several people who are not that good with their guns with imr white hots.
Wipe down the action and the outside of barrel too.  
Good luck down there.