Glenn,
Which of the stopovers are because are there purely because of flight timings for MR's and which are there because of Work/Personal interests/commitments?
For maximum miles/QF segments in N.America, why not do something like BDA-(JFK/MIA)-DFW-LAX-SFO-YVR-JFK which would yield just short of 7000 base miles, and set you up nicely for the QF108 JFK-SYD flight.
It would leave you circa 3200's short in comparison to your current N.American plans however JFK-SYD is 2500 base miles more than SFO-SYD so you'd only be losing out on 700 base miles and have SFO-YVR on QF, YVR-JFK on CX then effectively another transcon on QF before flying back to SYD. I'm sure it'd be far more comfortable than 6.5 hours each way on an MD83 between SFO & MSP
If you were looking at maximising mileage (assumes SJU, MSP were purely due to not being able to turnaround on flights) then a routing of something like;
MEL-SIN-HKG-(DPS/CTS)-HKG-SIN-FRA//LHR-AUH-LHR//LGW-BDA-(JFK/MIA)-DFW-LAX-SFO-YVR-JFK-SYD-PER-CBR-BNE-MEL
would give you 49811 base miles according to Mileage Monkey and have real first class on;
MEL-HKG
hkg-sin-hkg (if on flights operated by a 744)
HKG-FRA
LHR-AUH-LHR
LGW-BDA
mia-dfw (sometimes operated by a 777 with intl first class)
SFO-YVR
YVR-JFK
JFK-SYD
If you wanted to maximise first then i'd swap DPS/CTS with NRT - but note only on the some of the HKG-NRT-HKG flights is first class available.
The plus side is, maximum first class and of course not having to purchase an additional segment in N.Ameria. Also you will have 8 out of 20 flights on QF with 3 of those being intercontinental flights, so maximising any tier/cabin bonuses you maybe entitled to.
The downside is that according to the archived version of Mileage Monkey you cannot fly back into Oz and then out to AKL and back - i.e. once you have returned to the country of origin you cannot leave & re-enter. I'm not sure if this is correct - someone else will have to confirm. If of course getting to and from AKL is cruicial, then this plan/routing is pretty much useless....