One thing I have started doing that helps A LOT, is after cleaning, oiling, and wiping down, I allow the gun to sit for 48 hours with the muzzle down over a paper towel. (You can place it into a gun case with a piece of paper towel wrapped around the muzzle to prevent anything from soaking into the case itself). Then lean it against a corner of the room.
This allows any and all excess oil, solvent, and liquid to drain down out of the action, through the barrel into the paper towel. You'll be surprised at how much runs out. This prevents this excess liquid and lubricant from running into the action and soaking into the wood surrounding it. I even do it with AR's and other synthetic stocked weapons. Then after 48 hours, store the weapon normally.