You're right. But why so much work? A trivial modification to my code will do that.

sub fact7b {
    my @factor = map Math::BigInt->new($_), (2 .. shift);
    while(@factor > 1) {
        my @pair = splice @factor, 0, @factor / 2;
        $_ = $_ * pop @pair for @factor[0..$#pair];
    }
    return shift @factor;
}
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Update: doh, fixed overly clever, broken code. (s{1 + $#factor / 2}{@factor / 2})

Makeshifts last the longest.