How to pay apartment deposit w/ US bank account (Mumbai)

Hi all,

I'm expecting to sign a lease for an apartment in Dahisar on Thursday. I can't open an Indian bank account until I've already signed the lease and I can't sign the lease without being able to pay the deposit and first month's rent (total Rs. 120,000). I asked HSBC for a traveler's check; they referred me to Western Union, which referred me to ICICI, which referred me to Chase (my bank in the US) which doesn't have a retail branch in Mumbai and told me to get the amount in cash from a bank here. Even if I can pull that off, I would rather not be travelling around Mumbai with a brick of $ Protected content rupees.

Does anyone have any advice?