Stubble,
The things that have the greatest effect on the correct length of a stock (LOP/length of pull) are neck length, height of the gun mount and how close to parallel the sholders are with targets when you fire. (The usefulness of placing the gun in the crook of the arm to see if the trigger is in the right place for the trigger finger is an excellent way to determine the length of stock if, and only if, the gun will be shot that way and not mounted normally. Otherwise, it is completely useless.)
Guns with rising combs rather than those that are parallel with a gun's barrel, introduce another complexity. This is because the height of the eye relative to the rib, is determined by where on the comb the cheek makes contact when the gun is mounted.
To get back to your original question, longer-necked (usually taller) shooters need longer stocks. Trap shooters use longer stocks. Low, gun mounts require longer stocks. Shooters who face targets more directly need shorter stocks (with more cast.)
Recoil pads and spacers usually require the fitting of the pads and spacers (and longer screws) during installation. Fitting can be done by scribing a line arount them along the edge of the stock, removing the pad or spacer and rough sanding them to get them close. (Be careful to maintain the angle at the bottom of the stock/toe.)
Fine tuning of the final fit can then be done by carefully sanding the pad and spacer down to the stock after it has been taped to avoid damaging the finish. (You don't want to cut through the finish so close to the end-grain of the stock where water could easily infiltrate to swell and crack the wood.)
As was mentioned, this is best done using a rigid sanding disc. All in all, it is a job best left to someone who has had successful experience. If you have someone do it for you, ask them to check if the pitch on the stock is correct for you. 870s are notorious for having too little pitch. (The bottom [toe] of the stock sticks out too far.)
All this hasn't brought you any closer to learning just how long your stock needs to be. Mounting the gun with your eyes closed demonstrated that your cheek wound up farther forward on a higher part of the comb than it should be indicating that the stock is indeed too short for you. Just how much too short it is, is impossible to say. As was mentioned, the height of your gun mount and how you stand when you shoot are things that will affect your correct stock length.
Oh, yes: You have also demonstrated that a serious corruption of the way you shoot (shooting form) can "correct" things but don't expect to be able to hit anything if you shoot with the top (heel) of the pad above your shoulder. This holds true with other compensations for illfitting stock dimensions, as well. All affect shooting performace as compared to shooting potential.[urlhttp://stockfitting.virtualave.net[/url]