I’m sorry but it doesn’t make sense to me. Regardless of the month, I think what matters first is to know what day of the month you are in, if at the beginning, in the middle or at the end of said month. After you know that, you can find out the month to know where you are in the year.
What is the benefit of doing it the other way around?
Out of curiosity: do you also find it weird that (I’m assuming) you use hour:minute order when reading the clock, instead of minute:hour? Would saying the minute first make more sense to you?
This is already done often.
Quarter after 4 aka 4:15
10 to 5 aka 4:50.
Half past noon aka 12:30
No