Why not go thru Darwin to London?
According to Great Circle Mapper the great circle distance SYD to LHR is 9188 mms and goes nearly directly over Darwin.
Th GC distance SYD-DRW-LHR is 9191 mms.
The GC distance SYD-PER-LHR is 9602, 411 nms, or nearly one hours flying time, longer than going thru DRW.
DRW almost never gets fog and Tindal is less than 200nms away as a viable alternative and DRW already has a combined INTL/DOM terminal.
I'll wager that most of the pax to LHR would come from the East Coast Oz with a limited pickup from PER in any case.
Cheers,
BH.