Emirates Airlines Skywards - Tip for upgrading on a combination deal

I have purchased a combination fare to Australia (Y to DBX and J to SYD). However, it seems like it is hard to upgrade the LON - DBX part with points. Any advice on this? They said there is plenty J class available, but when I try to upgrade there are none :(
I am scheduled to fly tomorrow on EK4 but can change the flight if that would help.

Tommorow is showing:

[KVS Availability Tool 2.5.2/Platinum - Apollo: ITN/US-TNT] (http://KVS.UnrealNetwork.com/Tool/?R)
LHR London Heathrow UK [EGLL]
DXB Dubai AE [OMDB]
TUE 21 Nov 2006

Carrier Flight From Depart To Arrive A/C St Availability
--------- ------ ---- --------- ---- --------- ---- ---- ------------
EK 2 LHR 13:45 DXB 00:30 +1 77W 0 J0 C0
EK 8 LHR 08:30 DXB 19:25 332 0 J7 C9
EK 30 LHR 16:35 DXB 03:25 +1 772 0 J7 C9
EK 4 LHR 20:00 DXB 06:45 +1 77W 0 J0 C0
EK 6 LHR 22:00 DXB 08:45 +1 773 0 J0 C0


Therefore, I would try EK8 or EK30 if you want to upgrade. However, you would have a long wait in DXB.