Need some advice please.

We've finally decided to head to Australia and to NZ in September. We are co-inciding this with a family get together in Dubai for 5 days at the end September. The plan is to 3 days in Sydney and approx 10 days in NZ (Auckland and Christchurch) with the final 5 days in Dubai on the way back to London. Emirates is the logical choice but J is coming in at just over £4k from LHR.

I have decent stash of avios and a 2for1 voucher. I know I can use avios for flights between Australia and New Zealand (LATAM and Qantas). Are there any other ways I can best use my avios to get the cost down? We are London based but can be flexible on departure city and stopover :-)