Just one comment.
Because you are flying LHR-SYD you have to pay for the 4th continent (Asia)and because you are not having a stopover in Asia on that leg you are able to backtrack to Asia on the way back to North America.
So you could fly LHR-SYD-HKG-TPE-SJC and then upgrade your TPE-SJC AA segment or NRT-wherever AA fly from Tokyo.
If you want to maximise Q-points - well that requires a whole book.