Honestly to Bombay from SFO flight time/distance is 95% the same whether you go via atlantic or pacific. so your options are vast since now you can consider: Cathay Pacific, ANA, Asiana going west.

Also, keep in mind you dont have to fly one airline to go all the way. e.g. you can take AA to LHR then BA from LHR to BOM.

I'd say since you want two tickets in C/F it will be hard unless you get at least 3-4 cards ( assuming you have no miles at the moment)

Do you have any balances atm?