The consensus from travellers seems to be JQ do allow ODUs to Starclass, for anywhere between $200 and $300, or as much as the difference in fare. However, I have spoken to two different JQ phone operators this week and they both tell me that ODUs aren't possible. Maybe it's a secret!
Also, I'm on QF283, the JQ3 SYD-HNL codeshare service. This was booked from Australia and it isn't a FF redemption so it appears the codeshare can be booked in these circumstances.