On a cool Jan night had looked at similar "fantasy" (in my case) trip...
IAH > (DFW) > BNE (AA then QF)
BNE > AKL (QF)
AKL > SYD (QF)
SYD > PER (QF)
PER > HKG (QF)
HKG > JNB (CX)
JNB > CPT (BA - Comair)
CPT > LHR (BA)
LHR > IAH (BA)
Highest level available in each (of course) - so F wherever possible (it is fantasy trip after all).
Stops along the way - I looked at 22APR to 29MAY just to see if possible. (Didn't go obviously - well not this year anyway)