First off, kudos on that regex. Very spiffy. Are you aware of qr/REGEX/ in newer Perls?

As to the problem at hand, yes, you're going to have to use capturing parens and manipulate the results. Something like the following in your if condition:

if ((($month, $day, $year) = /($month)($day)($year)/io) ||
    (($day, $month, $year) = /($day)($month)($year)/io)) {
....
}
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Then, the question becomes, what goes in the "...."? I'll assume you have a plan in mind for $year, and $day doesn't require anything unless you want to do verification. My suggestion for $month is a hash that looks something like this:

             JANUARY  => 'Jan',
             FEB      => 'Feb',
             FEBRUARY => 'Feb',
             ....
             DEC      => 'Dec',
             DECEMBER => 'Dec');
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Then you can so something like:

printf('%02d-%s-%04d', $day, $mhash{uc $month}, $my_year);
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where $my_year is something you calculated from $year.

Of course, if you want to validate the day first, you could augment %mhash something like this:

my %mhash = (JAN      => {Name => 'Jan', Days => 31},
             ....
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And print like so:

printf('%02d-%s-%04d', $day, $mhash{uc $month}{Name}, $my_year);
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That was probably more answer than you needed, but there ya go.

*Woof*