Unicode has you covered!
https://en.wikipedia.org/wiki/Duodecimal
So M is one of {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ↊, ↋}.
U+218A ↊ TURNED DIGIT TWO
U+218B ↋ TURNED DIGIT THREE
There are other contenders for the 11th and 12th symbol, but all of those systems seem to assume counting from 0, which is... not a very fortunate choice: Human calendars generally numerate the first month as "1", not "0". So duodecimal does not get my vote for less ambiguity on either the account of determining what symbols to use, or where to start the sequence. :-)