i believe the C2 is a code from the plant, probably for who finished/ground it, or possibly who was running the forge. could also be who tempered it, as that may have been important when they sent out a bad batch and needed to know who to fire.
i have a woodslasher double bit with a "B37" as its only stamp/marking. i believe its from the era when they switched to only the paper decal and dropped the stamps all together. the B37 is in the same spot yours is, right square in the middle of the eye.