how about this, greenlee also had a 24" that said it was 5/16 but it didn't seem like it was 100% guaranteed but this looks like the ticket
Champion Proline 8800-24 24-Inch 5/16-Inch Hex Auger Bit Extension https://www.amazon.com/dp/B001TRF1XE/ref=cm_sw_r_other_apa_eJPzybKJRDJ1X
that looks just like what you linked to only longer so you may need to cut it down depending on the size of your lathe