Good call on doubling the string. Though the Schwartzian seems unnecessary here:

my $text2 = "$text$text";
my $tlen = length($text);
my $bwt7 = join('', 
        map{ substr($$_, -1) }
        sort{ $$a cmp $$b }
        map{ \substr($text2, $_, $tlen) } 0..$tlen-1
);
print "$text: $bwt7\n";
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Intermediate array of references consumes more memory than an array of offsets would, I think, but is faster to sort. Something to test and benchmark...