Re: Go for f if u can......
What routing are you coming up with for SYD-JNB...via SIN or BKK? Anyway, I don't think they're going to let you do SYD-JNB-LAX. That's about 160% longer (e.g. going SYD-SIN-JNB-LAX) than the direct route which has good availability on UA.
The argument might be "travel South Pacific to Africa return; first direct from South Pacific, second via USA with stopover in LA". Somehow, I don't think they are going to buy that.
They might "let"
Voodz do so but they may be tempted to charge on the Round The World rate which is 300k in Business - quite high.
The alternative is to book 2 return itineraries - one South Pacific to Africa (use NZ/SA), the other Africa to USA/Canada (use SA, MS or UA by transiting within the continent). That's 240k in Business altogether. Note that if your transits or stopovers touch other continents not covered by the primary destination and origin, then unless you have no choice or it is cheaper, they will force you to pay the higher charge or disallow the routing. This, of course, means that you will travel to South Africa, then to America, then back home, but not directly from America to Australia, but via (not necessarily South) Africa.
Getting from Australia to South Africa without touching Asia would involve getting yourself to PER (can't use *A direct) then SA from PER to JNB. An alternative is use NZ to fly to AKL (e.g. SYD-AKL), then connect to AKL-PER, followed by PER-JNB. If you try for Asia, as I said there may be extra or it may be disallowed.
From South Africa to USA, you can either use SA to fly direct from South Africa to USA (then use connecting flights on UA or US); or fly to LOS (Lagos) using SA, then UA to America; or fly to CAI (Cairo) using SA or MS, then MS to America. It all should be the same cost (except possibly for taxes) but US DM may force you on a particular routing (viz. the most direct one). If you touch Europe and they allow you without costing more, you have plenty more options (e.g. TK, LH, LX, OS and more transit points for UA and even US services - though availability is a whole different ball game).
If you can't have too many indirects, then at least one long flight must be on SA so I'd be tempted towards an all Business itinerary. The only F services from Australia to Africa are on SQ (near impossible to get) or TG (fairly easy to get) - both touch Asia. From Africa to America you will need to fly to Lagos (on SA, no F) or to Europe (only F carriers are LH or LX) to connect to an F service (UA from Lagos). This may be all too much trouble, availability of F is scarce on Trans-Atlantic LH and LX and there may be routing problems not worth the extra expense in points, so perhaps this is another reason to stick to Business only.