During the summer a black trash bag placed in direct sun will draw the stuff off the wood and it will run down into the bag. Unfortunately this will not work during December in Ohio or other cold places. This is where a blow drier used on hair works well, not a heat gun unless you want a scorched roasted stock. After the stock has given up so much oil and cosmoline the wood can be soaked for awhile in scalding hot water mixed with TSP (Tri Sodium Phosphate)
Yes, a rock to hold them down. The Scotch Brite is for an occasional scrub of the wood. About every 30 min for a few hours total. The TSP will draw the years of oil and dirt out of the stocks. Allow the wood to dry in the hot sun or overnight in front of a heater vent (Winter).
Start working on a nice oil finish of your choice, boiled linseed oil, tung oil or something like Birchwood Casey Tru-oil. Whatever trips your trigger.
Finally put the rifle together.
The trick is drawing the oils out of the wood once the surface stuff has been wiped down.
Brownell's Old Fashion Whiting is another good way to draw the grease and oil out of the wood.
Ron