The easiest solution is to make Tibet not exist on the board (and just replace it with a wasteland), honestly. It addresses the problem (nations crossing the Himalayas), but it's an unelegant solution, I feel.
That would also mean that historical invasions across the Himalayas (China and Tibet into Nepal and Bhutan for instance or the Nepalese Ghurkas invading Shigatse) would no longer be possible. The Mountains are already closed off in most places but the routes actually used by armies in the era are open.
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