Unfortunately, this does not work. The assignment of the wires does not match. In the standard VGA cable, wire 9 is not assigned, but this is required for the Logitech Z906.
Maybe you can get a high-frequency cable with full assignment and mini D-sub plug/socket somewhere.
However, I would like to point out that the cable length plays a role together with the cable quality and I don't know how much you can extend the cable without losing the signal.
But it would be cool if you find something that works.
Good luck.