Time and patience help alot, it is a slow process, I've had some that spent a month in the sun and another month in the heat of an attic. When in the attic, I had it wrapped in a Pig mat, a mat designed specifically to absorb oils/greases, and yet to this day, it will still ooze and get slimy when real hot. Brownells Whiting compound is pretty much a powder that absorbs oil, basically a surface treatment, it won't get down in the guts of wood, most paint/wood furniture places have a form of it. Murphys oil soap and damp hot rags or even a lemon/orange oil can help remove the oil and crap and not alter the wood color or finish, if nothing else it might smell better while your face is plastered next to it.
I've seen people get impatient and use EasyOff, Purple Power, even Oxalic Acid, all these do is either bleach the wood or burn the wood due to caustic chemicals which alters the appearance and wood coloration, and I have no idea how those would affect laminate or glue. Something like wipe downs with Simple Green would be an alternative to those harsher chemicals as well.
I would sweat the worst out, sun, attic, car, heat gun.... then start wiping down with Murphys oil soap/lemon/orange oils and wiping dry. Eventually it will really slow down the weeping and oozing, but, under the right circumstances it will ooze a little, besides..... a little grease never hurt nobody.