I'm not aware of the ins and outs of AA mileage redemptions, so forgive my ignorance but unless you are planning on stopping over en route why would you not look at ORD-DEL then get a cheap internal flight to BOM? I would have thought that'd give you the shortest travel time.
If you do look at going the LHR route then i'd strongly suggest you look at flying something like ORD-YYZ-LHR-BOM, taking the ORD-YYZ flight will allow for a T4-T4 connection at Heathrow, far more straightforward and far less hassle than having to connect via T3 - which is what an AA -> BA transfer will be.
When are you planning of travelling and what class?
CX have a new Y/J/F product rolling out and thus travel via LAX/SFO to HKG could be attractive if you are looking at travelling in 10-12 months time when more of the fleet have been kitted out.
Similarly with BA and the ongoing saga that is T5 - which (I believe ) is due to come into action in March 08. But that would be more of a gamble as it is likely to either be an utter shambles highlighting the general incompetency of BAA

or it'll be a dream come true. Fingers crossed for the latter! ^