If you wanted to maximize skymiles you could do JFK-ATL-DXB-MAA with ATL-DXB on Delta. I mean I wouldn't recommend it but you do have some options. I have seen tickets on OTAs (atleast in Y) so I would assume you could check bags through. You could also fly to BLR with AirFrance which is pretty close to MAA and take a short one hr flight/5-6 hr train to MAA.

Otherwise credit to Alaska. You'll get 125% Miles(which is bad for a premium cabin but better than nothing). You could also status match with Alaska (note its a onetime per lifetime thing so don't do it if you want to get Alaska status the easy way) and get a 100% RDM miles bonus. You'll get MVP-G status for your Delta Plat without a status challenge. You could redeem Alaska for AA, DL and whole bunch of Skyteam Oneworld partners. Emirates redemptions is scheduled for late 2012 but it looks it might take some time.