A few routes:
(1) ARN-LHR-MCT-LHR-SYD-PER-ALS-MEL-SYD-HKG-NRT-SIN-NRT-HKG-LHR-ARN 45,423 miles 9 legs in true F
http://gc.kls2.com/cgi-bin/gc?PATH=A...OR=&MAP-STYLE=
(2) ARN-LHR-MCT(or CAI)-LHR-SYD-PER-ALS-MEL-SYD-HKG-NRT-SIN-NRT-HKG-JFK-LAX-DEN-MIA-ORD-LHR-ARN
57,695 miles 11 legs in true F
http://gc.kls2.com/cgi-bin/gc?PATH=A...OR=&MAP-STYLE=
(3) DEN(o)-LAX(o)-LHR(x)-MCT(or CAI)(x)-LON(x)-TFS(x)-LON(x)-HKG(x)-NRT(x)-SIN(x)-HKG-NRT(x)-JFK-SJU(x)-JFK(o)-LAX(o)-DEN(x)-MIA
46,768 miles 10 legs in true F
http://gc.kls2.com/cgi-bin/gc?PATH=D...OR=&MAP-STYLE=
(4) ARN(o)-LHR(o)-MCT(or CAI)(x)-LHR(x)-HKG(x)-NRT(x)-SIN(x)-HKG(o)-NRT(x)-JFK(x)-SJU(x)-JFK(o)-LAX(o)-DEN(x)-DFW(o)-YVR(x)-LHR(o)-ARN
44064 miles 10 legs in true F
http://gc.kls2.com/cgi-bin/gc?PATH=A...OR=&MAP-STYLE=