use constant MONTHS => 'JanFebMarAprMayJunJulAugSepOctNovDec';
...
my $month_num = index(MONTHS, $month_str)/3;
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Better still?

Unfortunately, this (against my expectations) turns out to be between 30% & 50% slower than the hash solution.

It uses much less momory, but it seems that hashing a 3 char string, indexing and returning the value is faster than a linear search for a 3 char string + a division.

Surprised me