I think you are right that they often don't want to be recognized as Indians except when it suits them, but figured it might help. I don't know... don't have many great ideas. It's a depressing situation.
Anyway, this is the list I have:
Sundar Pichai (Google)
Satya Nadella (Microsoft)
Shantanu Narayen (Adobe)
Ajay Banga (Mastercard)
Aneel Bhusri (Workday)
Nikesh Arora (Palo Alto Networks, ex Google)
Ajit Jain (Berkshire Hathway)
Sanjay Jha (Global Foundries)
Vinod Khosla (Khosla Ventures, ex Sun)
Thomas Kurian (Google Cloud, ex Oracle)
Dinesh Paliwal (Harman International)
Sanjay Mehrotra (Sandisk)
Ram Shriram (Sherpalo Ventures)
Non-business luminaries who might be helpful:
Abhijit Banerjee (Nobel Laureate in Economics)
Nitin Nohria (Dean of HBS)
Ex business people:
Vikram Pandit (ex Citi)
Indra Nooyi (ex Pepsi)
Kanwal Rekhi (TiE Co-founder)
I used this
list for ideas.
Edit: The list of successful Indian Americans is pretty darn impressive, and yet we are stuck in this stupid effing backlog.