I would just modify any single digits before parsing.

johngg@shiraz:~/perl/Monks$ perl -Mstrict -Mwarnings -E '
my @dateStrs = (
   q{Fri May 8, 2020 - 11:12:13},
   q{Fri May 15, 2020 - 14:08:17},
   q{Sat May 16, 2020 - 7:31:22},
   q{Mon Jun 1, 2020 - 6:24:18},
   );

s{(?<=\D)(\d)(?=\D)}{ sprintf q{%02d}, $1 }eg for @dateStrs;
say for @dateStrs;'
Fri May 08, 2020 - 11:12:13
Fri May 15, 2020 - 14:08:17
Sat May 16, 2020 - 07:31:22
Mon Jun 01, 2020 - 06:24:18
[download]

Perhaps the problem is more complex than stated in the OP but this seems to work.

Update: A version that copes properly with extra spaces, the first version didn't.

johngg@shiraz:~/perl/Monks$ perl -Mstrict -Mwarnings -E '
my @dateStrs = (
   q{Fri May 8, 2020 - 11:12:13},
   q{Fri May 15, 2020 - 14:08:17},
   q{Sat May 16, 2020 - 7:31:22},
   q{Mon Jun 1, 2020 - 6:24:18},
   q{Fri May  8, 2020 - 11:12:13},
   q{Fri May 15, 2020 - 14:08:17},
   q{Sat May 16, 2020 -  7:31:22},
   q{Mon Jun  1, 2020 -  6:24:18},
   );

s{(\s+\d)(?=\D)}{ sprintf q{ %02d}, $1 }xeg for @dateStrs;

say for @dateStrs;'
Fri May 08, 2020 - 11:12:13
Fri May 15, 2020 - 14:08:17
Sat May 16, 2020 - 07:31:22
Mon Jun 01, 2020 - 06:24:18
Fri May 08, 2020 - 11:12:13
Fri May 15, 2020 - 14:08:17
Sat May 16, 2020 - 07:31:22
Mon Jun 01, 2020 - 06:24:18
[download]