India should help China and Tibet deal with each other. India should ask China to consider releasing the southern 1/3rd of Tibet SAR (Approx. 400,000 sq km) incl. Lhasa as a free nation and keep the rest. In turn, Tibet will accept the rest as an integral and unconditional part of China.

It is a win-win-win.

For China

Eliminates the unnecessary irritant of Tibet as a bugbear in its relationships with the rest of the world
Demonstrates to Taiwan and the rest of Asia their commitment to peaceful solutions
Lets them keep over 80% of the territory it occupied since 1951 including critical sources of Yangtze Kiang, Yellow and Mekong rivers

For Tibet

They get their own nation
The best deal they can get

For India

Allows India to solve the Tibet issue without affecting relations with China
Demonstrates India's rise as an important power
With Southern Tibet gone, China's need to hold on to Aksai Chin goes down and allows India to settle this issue by offering Tawang in return

A non-Chinese Tibet opens up a military corridor into China in the event of an invasion. That's a big reason the Chinese won't allow independence in Tibet. How would this action address that?

Good point. Tibet could sign a treaty with China that it will not allow its territory to be used in a future war against China under the condition that China would never invade Tibet again.