You can buy 2 extra segments per continent but not in your continent of origin (which sadly is NA in this routing). So the 6 segments for NA is a hard limit (along with 2 stopovers). Presuming you didn't want a 2nd LAX stopover, you could revise the routing to be bos-lax-ord-anc-ord-tpa-jfk-syd-akl-bne-per-dps-hkg-bkk-lhr-bos which reduces it to 6 segments and actually increases the mileage along with better comfort (but JFK-SYD operates only 3 days a week).