Other than perhaps having to buy BLR-DEL segment, wouldn't this be a classical good use of a RTW ticket?
i.e. OneWorld:
SEA-ORD-LHR-AMS
AMS-LHR-DEL
DEL-BLR
BLR-HKG-SIN
SIN-HKG-LAX-SEA
I am not as familiar with other RTW products, but I know you could make AA plat by flying this route.