I tried to minimally change your prog, but I think it is also ugly yet. Unfortunately Regexp::Common::balanced always quotemeta its begin and end settings, so you cannot change behaviour right there.

...
while ($text =~ m/$inpattern/xmsg) {
    my $first = substr $1, 1, -1;
    my $second = substr $2, 1, -1;
    $outpattern =~ s/\$1/$first/xmsg;
    $outpattern =~ s/\$2/$second/xmsg;
}
$text =~ s/$inpattern/$outpattern/gee;
...
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