I usually use Pledge on my stocks, but if I can get the stock separated from the receiver with that band that's pinned in place without damaging it I was thinking about working this stock over with some Murphy's Oil Soap to try and clean it up & get some of this black crud off of it because the front of the stock has a really nice cherry color to it but the further back you go the more it fades into a black on to the butt stock
Agree with Murphy's oil soap to start--helps get surface grime off. After dismounting the stock, then try odorless mineral spirits to more thoroughly clean the stock. Turpentine is a bit stronger cleaner but much more flammable. Neither solvent damages or swells the wood which is why I use them but they may remove any ersatz finishes applied. Depending on the degree of cosmolene soak, you may have to sweat the stock either chemically using a solvent and whiting or through heat (classic way is to put in a black sealed trashbag inside a car on a sunny day (in a warm climate).
Be careful removing the stock as the critical part most damaged in the Enfield series is that area just in front of Gunny's pix. These are the draws where the rear base of the receiver rests and are critical to avoid stock damage and inaccuracy. This area is often damaged through excessive oil seepage and improper stock mounting and subsequent recoil. This is also why YOU FOLLOW Gunny's pictures and instructions on how to dismount the forend--never try to lever it off. Don't ask me how I know--fortunately it was a sportered front end I was removing anyway.
Peter Laidler has a whole set of stickies on the subject of care and fitting of Enfields on milsurps.com in the Enfield subforum https://www.milsurps.com/showthread.php?t=16948 or Gunny, I'm sure has similar pictures from his stock restorations.
You may also find some damage at the front screw (king screw) of the receiver. A lot of times, the relatively thin area of wood between the king screw and magazine is damaged or missing.