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use strict;
...
 substr($str, $-[1],$+[1]-$-[1]) = uc $1;
 pos($str) = $+[1];
}

$str =~ s/(^|\G$RE{balanced}{-parens=>'<>'})([^<]+)/\U$1\E$2/g;
# Again? (and now I feel a DUH! coming on (:
$str =~ s/($RE{balanced}{-parens=>'<>'})/\U$1/g;