Since the grease hole is some NC/TN rifles is at an angle, my thought was to start the hole perpindicular to the center line of the stock, then swing the brace toward the butt end of the stock. This is what spoon-bits are designed to do, but I don't know if such a severe angle change would cause chip-out or even split the stock. Definitely have to try it out on some scrap first, after I get a spoon bit.
Yes, I've seen the pics of marks from different styles of bits in the bottom of patchbox holes too, but thought a spoon bit might leave a smoother bottom, without holes or crevices to allow patch grease to soak into. Maybe not a concern since you are putting grease into a hole in the stock anyway, or will natural tallow/wax types not cause any issues with the wood. Or I'm just waaaay over-thinking this.