Looking at it from just a miles perspective and using ExpertFlyer to determine all possible connecting points...
Code:
>> cxmiles LAX DEL ORD HKG MUC EWR FRA ICN LHR DXB PVG SVO BKK
Route Leg 1 Leg 2 Total R/T
LAX-DEL 8013 16026
LAX-SVO-DEL 6078 2714 8792 17584
LAX-ICN-DEL 5994 2896 8890 17780
LAX-PVG-DEL 6485 2671 9156 18312
LAX-ORD-DEL 1744 7484 9228 18456
LAX-HKG-DEL 7260 2331 9591 19182
LAX-FRA-DEL 5806 3812 9618 19236
LAX-LHR-DEL 5456 4191 9647 19294
LAX-MUC-DEL 5989 3673 9662 19324
LAX-DXB-DEL 8339 1360 9699 19398
LAX-EWR-DEL 2454 7324 9778 19556
LAX-BKK-DEL 8270 1831 10101 20202