One other comment about the "Economite Hoard", those were mostly half dollars not quarters., and they were not punched with a L or E, they tended to have a single vertical punch mark, like with a standard screwdriver, at 12 oclock on the obv.
The L and E quarters only come dated 1815 or 1825 and the letter punches are the same on both dates. The placement of the E and L differ, but the E's are in the same place on both dates, and the L's are in the same place on both dates. The coins were probably stamped while on a medium hardness wood block that was able to conform to the shape of the rev and support it as there is very little damage to the reverse from the stamping.