It's 5 zones (Europe, N America, S America, SW Pacific, Asia).

Otherwise as an itinerary I think it's OK. You don't need to worry about stopover vs transit except in N America (only two stopovers allowed) and when reentering a continent for the second time when in transit somewhere else (where allowed). So your SYD-LHR goes through Asia which must only be a transit.

There are lots of ways to get more miles, but since you are time constrained at each ened you may not be able to fit them in.

Since you don't need to go to Europe, consider whether you could squeeze all this into a CIR29 Circle Pacific fare which could be used to reach all of your required destinations if you can meet the mileage constraint. Not sure offhand of the relative pricing ex-US. However, I can't get it in the 29K at a quick look.