Don't have any specific advice for you but a couple of thoughts.

-Cheaper excursion fares usually have a one month max. Your dates are for aout 35 days. When it comes down to paying for the flight that you decide to pay for, make sure to check fares for one month or less andadjust your dates if at all possible.

-You are going to have to rely on two things. Cheap flight availability and Award travel availabilty and try to find that magic spot where they overlap.
Not sure if london is a good bet because there is so much capacity NYC-LON or bad cuz it's summer.

Not sure about the VS program, but keep in mind that on some airlines, for 50K you can get to London or to Moscow or Istanbul... both a good bit closer to India and maybe cheaper.

Also, I would check out the Indian discount airlines Jet, etc. and see where they have cheap flights from, then see about getting there... might mean award tix to London, then EasyJet to Rome or something crazy like that.

-See if there is award availability or cheap tix all the way and try to barter somewhere your $$ for miles (or vice versa) that's generally against the rules, but people do it. (Check Craigslist for example)

Edited to add : And welcome to FT!