1. There is no need to pay for EF - all awards are online at united.com, EF will not give you access to more awards.

2. Just book whataver business awards you can find with connections (via FRA, IST, CAI, ZRH etc) on NYC-BOM, and if it becomes available, call in to switch to the nonstop. Change fees will apply.

In theory, one can also book awards over the phone on Jet Airways, which would be very convenient in your situation.