Lima 8 Reales 1824 J.m. - Overstruck Over Another Coin?

I was looking at this 8 Reales Lima Mint 1824 J.M in my collection this morning and for the first time notice that it seems to have been struck over another coin.

This seems very plausible given the chaotic conditions which must have existed in Lima in the year 1824. That was a year which was to culminate with the ultimate defeat of the Spanish in the viceroyalty of Peru. This was the last 8 reales struck in Lima with the bust of Ferdinand VII. It makes sense therefore that the loyalists would grab whatever coinage was available and overstrike with the emblem of the spanish King. They had done that when countermarking the Peru Libre coinage of 1823.

The under type can only be seen, at least by me, as a letter M under DEI on the obverse. It is weak but it is there. I have searched for coins of that period which may have had an M somewhere in the legend, but no luck so far. One possibility may be coins bearing the LMAE in ligature as symbol for the Lima mint, but it does not seem to be that.

Interesting little tidbit of history.

Does anybody have any other ideas?