I just did three DONE4 bare-bones dummy bookings to see the impact of first/ticketing carrier choices. I tried a fourth, with JNB-DOH as the first flight but the tool balked as usual.

JNB-SYD-LAX-JFK-LHR-JNB (QF as first/issuer) - ZAR 76,279 (USD 5034) of which ZAR 7196 ($475) was carrier-imposed fees.

JNB-HKG-LAX-JFK-LHR-JNB (CX) - ZAR 68,536 (USD 4523) of which ZAR 3396 ($234) was carrier-imposed fees.

JNB-LHR-LAX-JFK-HKG-JNB (BA) - ZAR 71,782 (USD 4738) of which ZAR 3580 ($236) was carrier-imposed fees.

Note I used AA metal on SYD-LAX, JFK-LHR and LHR-LAX in these scenarios.

Curiously, the base fare was the same - ZAR 58,940 - in the first two runs, but was ZAR 59,020 in the BA run. Huh?

Anyway, bottom line, CX was the cheapest but not by much. Presumably if one populated the QF and BA itineraries with more flights a greater disparity would appear, but it's hard to say how big a deal it would be. Certainly $240 or so of spread on a $5000 ticket isn't a deal breaker in my mind.