I recently flew ORD-LHR-BOM on AA/BA and the T3-T4 transit literally took over two hours of standing in security lines. The problem with transit in DEL is that you'll likely need to stay overnight due to the arrival time of the AA flight.
While the LHR transit option is inconvenient, I think it's the most reliable because BA was pulling people out of line who risked missing their flights.
Keep in mind that LHR enforces the 1 carry on bag rule VERY aggressively.
If transitting via LHR i'd strongly suggest the OP looks at ORD-YYZ-LHR-BOM as that way they will have a T4-T4 connection which will be far smoother than the T3-T4 nightmare.
If you can get on the earlier YYZ flight it will give you a 4 hour layover which is enough to 'whizz' through customs (BA J/F pax who have a non-eu passport get access to fast track customs) to the airside arrivals lounge where you can enjoy a power shower, get your clothing pressed and take advantage of a full breakfast spread as opposed to the grease-laden CW breakfast that is all too common.
You'll have plenty of time to make your way back air side, again, via 'fast track' the Gate 1 Terraces lounge is excellent and the least crowded of the T4 lounges. In recent months they have started serving hot food throughout the day in buffet style. Unlike AA all lounges feature an open bar. Champagne is available by the glass on request.
If you can sleep on planes then a direct ORD-LHR-BOM might not be too bad as you could get the red-eye from ORD with AA, head into central London for lunch/sightseeing then catch the evening flight to BOM which will get you into BOM for late morning as opposed to the early hours.
Finally, as already mentioned AY are due to start flying HEL-BOM later in the year. The connection times are rubbish, but if you fancy a day in HEL then go for it. I've neither experienced HEL nor AY but don't think I have heard a bad word about them on this board. It looks as though the one of their 343 aircraft are scheduled to fly the route and i'm not sure whether these have the new lie-flat shell-seats installed. One of the experts out there will be able to clarify though i'm sure!