This is very similar to the method I use and, after conversation with him, the method Art Benjamin uses. It's trivial to do in 10 to 15 seconds, though it requires practice, a very small amount of memorisation[0], and a small amount of mental arithmetic. I use it regularly, partly to keep in practice, and partly because once you have the skill you find it's surprisingly useful. JH Conway used a different technique[1]…
I don't quite understand. Your magic month numbers are 3 digits, but you only use one digit in your example. And how does substituting 2012 work, when 2012 was a leap year but 1900 wasn't?
So Jan=1, Feb=4, Mar=4
> 025 : Apr, May, Jun
So Apr=0, May=2, Jun=5
... and so on.
And we can substitute 2012 for 1900 because we make a correction in Jan and Feb in leap years. Knowing that 1900 was not a leap year means we don't make the correction, but 2012 was a leap year so we do.