ITA (which I tend to use) doesn't find this on a simple LHR-SYD-LHR search in business class, even though it is cheaper than all the other options.

However, a forced routing on Finnair:

from LHR:: AY AY AY
to SYD:: AY AY AY

Brings up all the options you mentioned. Looks like it is LHR-HEL-(HKG/BKK)-SYD-(HKG/BKK)-HEL-LHR. So you can try BA, CX and AY longhaul, together with BA and AY shorthaul in one return journey if you want. The connections are decent as well, it allows 4 free stopovers and you can arrive into SYD in the evening if you take the day flight from HKG on CX....

Or even:

from LHR:: AY AY AY AY
to SYD:: AY AY AY AY

Which brings back LHR-HEL-BKK-HKG-SYD-BKK-HKG-HEL-LHR

or

LHR-HEL-BKK-HKG-SYD-BKK-HEL-ARN-LHR

Not bad at 640 tier points for £2,800 and less than 48 hours notice. But wait, there is more for 720 tier points

from LHR:: AY AY AY AY AY
to SYD:: AY AY AY AY AY

LHR-ARN-HEL-HKG-BKK-SYD-HKG-BKK-HEL-ARN-LHR

An excellent price for 10 segments, which allows for shorthaul AY and BA and Longhaul BA, CX and AY.