oneworld - Europe-Dubai award - what routing?

As part of a oneworld award itinerary, I am looking at going from Europe to Dubai. BA's LHR-DXB flights seem to have very sparse award availability, even in Feb 06 when I am looking. Are there any other options or suggestions?

On that, where can I check BA award availability?

Can you book a oneworld award on Finnair leisure sectors (ops 2x weekly HEL-DXB)?

Whick program are you using for the reward? QF, BA or AA or ?
Do you have any FF status ?
With QF always get better results phoning them

I'm QF and just have silver status (only real advantage is avoiding long waits on the phone!)

BA has other flights to cities near DXB, for example Doha (circa 200 miles from DXB). There are 3 or 4 choices and they might be easier (but knowing BA, probably not). Depends on your visa requirements, available time and travel budget.

AUH might be a better bet; you can drive to Dubai in an hour or so.
If using a oneworld award (with AA miles), you could also route Europe-HKG-DXB if not stopping over in HKG. AY also fly to DXB, but it is seasonal (and all economy)