I reguarly do this route, (ATL-BOM), I have good luck out of MIA and DFW, using the SWU,
to LHR, both those routes have the 77W, which for me is a better craft to use the SWU,
ORD still uses the 777, which if you get stuck in a middle seat, to me its not worth it.
BA out of LHR, has 2 departures, 10.35am and 9.25pm, I have taken both, and the past 4 trips I have taken this year, the flight has had a light load, the last trip I took in April on the 777 had only 56 passengers, so it was a breeze to get a whole row to myself,
beware though, on the BA 777 , the armrest do not go up all the way.. making sleeping ,
somewhat cramped.
If I had the time I would do the CX routing, but since my visits to India are only for a few days, BA works out fine, plus you will find the Frist class lounge out of T-5 quite decent.