DEN-JFK-HKG-BKK-NRT-SIN-HKG-SYD-ZQN-SYD-CNS-MEL-LHR-DME-AMM-DXB-LHR-YVR-JFK-MIA-DEN comes to around 56,500 miles. 7 flights of 20 in J, the rest in F.

As no QF "domestic" routes in Oz/NZ have F I've included ZQN instead of PER and ADL as you'd be doing this trip in the northern winter/southern summer in which case visiting the Fjord country on the S. Island of NZ might be a nice counterpoint to steamy and/or desert locations. CNS is thrown in instead of BNE on the chance you want to see the Great Barrier Reef or Daintree country.

NRT-HKG-SIN-BKK-HKG-SYD-ZQN-SYD-CNS-MEL-LHR-DME-AMM-DXB-LHR-YVR-JFK-MIA-DEN-JFK-NRT is another approach (about 52K miles) in case you want to start in Japan for a cheaper AONE4 price (or way cheaper DONE4.) However you'd have to decide which 2 places in Asia to use for stopovers, just as you'd need to decide which two stopovers to take in N. America if you originate there.