Update: Originally solved the wrong problem. This version may be computationally simple enough that the ST suggested by others is unnecessary.

print sort {
   if (($a=~/^[a-z]/) == ($b=~/^[a-z]/)) { $a cmp $b }
   else { $b cmp $a }
} @needs_sorting;
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If the initial letters are the same case, sort normally
If not, sort reverse (putting the lower first).

Further update: I liked Broquaint's way of checking initial case.