If your aim is to get a free F class SYD-LHR after one RTW ticket, forget the QFF program.
Its possible with AAdvantage as follows:
Become Platinum by doing the Plat. Challenge giving you a 100% mileage bonus plus an extra 25% for cashing in your domestic upgrade certificates (which you won't earn the next year if you become Exec Plat! So you have to keep your Qpoints below 100000)
On a 5 continent RTW limited by the 20 segments you can probably eak out 60000-70000 miles at a push.
If you look at 60000 miles sticking to 1st class flights (hard to do) you're looking at earning :
60000 miles
30000 miles 1st class bonus
60000 miles Platinum bonus
15000 cashing in your upgrade certificates
Total 165000 AAdvantage miles
Miles required for SYD-LHR award in 1st 160000 voila!

The business class to HNL will not help nor will skipping South America which is better than Africa for high earning sectors.

The following route is an example using 5 continents:
20 segment path: 71651 mi
SYD (33°56'46"S 151°10'38"E) JFK (40°38'23"N 73°46'44"W) 9950 mi
JFK (40°38'23"N 73°46'44"W) SCL (33°23'35"S 70°47'09"W) 5097 mi
SCL (33°23'35"S 70°47'09"W) BOG (04°42'06"N 74°08'49"W) 2629 mi
BOG (04°42'06"N 74°08'49"W) SCL (33°23'35"S 70°47'09"W) 2629 mi
SCL (33°23'35"S 70°47'09"W) CCS (10°36'11"N 66°59'26"W) 3036 mi
CCS (10°36'11"N 66°59'26"W) SCL (33°23'35"S 70°47'09"W) 3036 mi
SCL (33°23'35"S 70°47'09"W) LAX (33°56'33"N 118°24'29"W) 5569 mi
LAX (33°56'33"N 118°24'29"W) JFK (40°38'23"N 73°46'44"W) 2475 mi
JFK (40°38'23"N 73°46'44"W) SJU (18°26'22"N 66°00'07"W) 1598 mi
SJU (18°26'22"N 66°00'07"W) ORD (41°58'43"N 87°54'17"W) 2072 mi
ORD (41°58'43"N 87°54'17"W) LAX (33°56'33"N 118°24'29"W) 1745 mi
LAX (33°56'33"N 118°24'29"W) ORD (41°58'43"N 87°54'17"W) 1745 mi
ORD (41°58'43"N 87°54'17"W) LAX (33°56'33"N 118°24'29"W) 1745 mi
LAX (33°56'33"N 118°24'29"W) LHR (51°28'39"N 00°27'41"W) 5456 mi
LHR (51°28'39"N 00°27'41"W) IST (40°58'37"N 28°49'16"E) 1565 mi
IST (40°58'37"N 28°49'16"E) LHR (51°28'39"N 00°27'41"W) 1565 mi
LHR (51°28'39"N 00°27'41"W) MCT (23°35'36"N 58°17'04"E) 3629 mi
MCT (23°35'36"N 58°17'04"E) LHR (51°28'39"N 00°27'41"W) 3629 mi
LHR (51°28'39"N 00°27'41"W) JNB (26°08'21"S 28°14'46"E) 5621 mi
JNB (26°08'21"S 28°14'46"E) SYD (33°56'46"S 151°10'38"E) 6862 mi


With your restrictions you're looking at the following with a lot of it in D:
20 segment path: 53710 mi
SYD (33°56'46"S 151°10'38"E) HNL (21°19'07"N 157°55'21"W) 5066 mi
HNL (21°19'07"N 157°55'21"W) ORD (41°58'43"N 87°54'17"W) 4244 mi
ORD (41°58'43"N 87°54'17"W) ORF (36°53'41"N 76°12'04"W) 717 mi
ORF (36°53'41"N 76°12'04"W) ORD (41°58'43"N 87°54'17"W) 717 mi
ORD (41°58'43"N 87°54'17"W) YYZ (43°40'38"N 79°37'50"W) 436 mi
YYZ (43°40'38"N 79°37'50"W) LHR (51°28'39"N 00°27'41"W) 3556 mi
LHR (51°28'39"N 00°27'41"W) MCT (23°35'36"N 58°17'04"E) 3629 mi
MCT (23°35'36"N 58°17'04"E) LHR (51°28'39"N 00°27'41"W) 3629 mi
LHR (51°28'39"N 00°27'41"W) IST (40°58'37"N 28°49'16"E) 1565 mi
IST (40°58'37"N 28°49'16"E) LHR (51°28'39"N 00°27'41"W) 1565 mi
LHR (51°28'39"N 00°27'41"W) CPT (33°57'53"S 18°36'06"E) 5994 mi
CPT (33°57'53"S 18°36'06"E) JNB (26°08'21"S 28°14'46"E) 789 mi
JNB (26°08'21"S 28°14'46"E) HKG (22°18'32"N 113°54'53"E) 6631 mi
HKG (22°18'32"N 113°54'53"E) NRT (35°45'53"N 140°23'11"E) 1842 mi
NRT (35°45'53"N 140°23'11"E) HKG (22°18'32"N 113°54'53"E) 1842 mi
HKG (22°18'32"N 113°54'53"E) SIN (01°21'21"N 103°59'15"E) 1588 mi
SIN (01°21'21"N 103°59'15"E) HKG (22°18'32"N 113°54'53"E) 1588 mi
HKG (22°18'32"N 113°54'53"E) MEL (37°40'24"S 144°50'36"E) 4590 mi
MEL (37°40'24"S 144°50'36"E) PER (31°56'25"S 115°58'01"E) 1681 mi
PER (31°56'25"S 115°58'01"E) SYD (33°56'46"S 151°10'38"E) 2041 mi