My opinion is that this gun as with many BSA pre WW1 types have been kicking around for up to a century, until recently they are collectible. Most of these guns ended up on farms usually ended up being abused during their life time, missing screws bodged up parts missing sights you name it, every thing you can think of, concerning bodging has been done,count yourself very lucky if you manage to get hold of a BSA in 100% condition. I myself have a few of these wonderful guns in my collection and as a youngster in the past have abused and bodged one in my youth to get the gun working when money or spares were a problem(shame on me). One thing i can guarantee is that when BSA made your gun in its hay day they certainly didn't send it out of the factory in a poor finish, they had very high standards. What you are experiencing with your gun as many that come by them, is years of abuse.
Most people try and replicate the original finish that is difficult to d, as it should be the same as the finish of the old WW1 Webley revolvers a blue/grey, very difficult to replicate, most finishes i have seen are of the modern day blue/ black done professionally with bluing salts in a hot bath, even worse with GM93 bluing paste.
Pitting is a gun finish down fall. Even with the best intentions of the owner to re-blue the gun, pits spoil the end finish. Polishing out pits not only thins the surface but some pits can be very deep especially when edges and profiles of the gun that should be sharp are rounded off during polishing. Painting may sound a good idea but i would steer well away from a gun with such a finish but if you do go down this route use Suncorite a military paint finish used by the Army. This finish sticks very well to metal and is difficult to remove when the metal surface is properly prepared, no need for primers. If you go down this route phosphate or parkerize the metal for a 100% bond. I would personally phosphate or parkerize a very pitted gun and leave the finish at that (not paint it) as it does blemish out the smaller pits and the finish doesn't high light them as would bluing. If you venture down this route you need to blast clean the rust and crud off but with a glass bead or the finest grit, this would get right into the pits to remove the rust, the phosphate finish actually look very professional (its a military gun finish anyway) and does suit the gun especially if you are going to use the gun ie for classic target shooting etc. There is not much you can do with a pitted gun especially if you intend to gain a 100% original finish. Best to save your money up and buy a minter.