Check out Ola. It does not require any credit cards or that annoying two step verification as paying by cash is so easy (and still preferred method) in India. Many drivers sign up for both Ola and Uber simultaneously. So there is no such things as Uber cars/drivers vs Ola car/drivers. Rates from both companies are ridiculously cheap. Ola customer service seemed to be better than Uber. You get electronic receipts for reimbursement any way.

The only hassle is that you need local India phone number. (everyone in India from doctor to dhobi to Ola to bank seem to insist on getting your "Mobile" number while bureaucrats babus want to deactivate your SIM moment you are out of country for 45-60-90 days)