Without concern for the airlines you fly on and not all in first class
DFW-NRT-HKG-KUL-HKG-SYD-JNB-LHR-DFW

Its about 33,000 miles and I doubt you will find a routing that is significantly less if at all. The only caveats are that you will be flying AA transpacific and if you are doing first class, the SYD-JNB is a two class aircraft. To rectify both situations, you would be able to do DFW-LAX-SYD-HKG-NRT-HKG-KUL-HKG-JNB-LHR-DFW which would be a slight over 37,000. Since the cutoff is at 35,000 miles, the second itinerary would cost more miles, but not significantly more, imo. Finally, combining the two of all first class and AA transpacific, you would get DFW-NRT-HKG-KUL-HKG-SYD-HKG-JNB-LHR-DFW which would also be about 37,000 flight miles. Hope that makes sense and hope it helps.