I finalized my booking yesterday -- here is what we ended up with:
ORD-LIS
MXP-SIN
DPS-SIN
SIN-BNE
SYD-WLG
PPT-SFO

Great Circle Mapper had shown a total of 21,883 including one more SIN-DPS segment but the ANA calculation was slightly different so we dropped that over the phone. We are traveling as a family of 4 and opted to book in economy for 85,000 miles each.

Fees came to $618 for adults and $543 for the kids. Total YQ for our routing was $280.

We originally had planned to go ORD-LHR on UA but that added $400 of additional fees compared to the TAP flight (total of $1010). The YQ on TAP (According to ITA Matrix) is actually $7 higher than the ORD-LHR flight so I don't know how that extra $400 was calculated. I also asked them to recalculate total fees if we also dropped the DPS-SIN leg but somehow they came back and told me the fees would be $800+ for dropping that leg. I asked how that could be and she went back to ticketing to double check and they said they were wrong it would be $720. That was still $100 more than what they had quoted me if I included that DPS-SIN leg so we opted to keep that leg in.

We will piece together budget airlines for Europe, SE Asia, and within Australia. I also booked AKL-PPT for 15k AA miles each.

Happy to be done and ticketed! Looking forward to our 3 month trip!