Your kind have proved me wrong in the past, so I will give you a chance to do so again.
The titan structure which houses the Engine of Nalak'sha spans the entirety of Pandaria. There are more ways to reach it than just the Mogu'shan Vaults.
There are many such routes, but the closest would be through Mogu'shan Palace. The chambers beneath the palace are interconnected with the vaults.
Seek your fate there, champion.