UK passport holder. Seoul-Shanghai(3 days)-Birmingham.does 72 or 144hr free transit visa apply?

We are planning to use your flights for the below itinerary and are planning to arrive in Shanghai. We want to apply for the 144hr free transit policy. We will be flying from Birmingham to Tokyo, Tokyo to Seoul and Seoul to Shanghai (for 3 days), then back to Birmingham, U.K. ( via Amsterdam).
Does the 144hr transit apply? I have been advised it does not as we are returning from Shanghai to Birmingham, (our home country ) even though this is will be via a connection through Amsterdam.
If we change our route to Birmingham to Tokyo, Tokyo to Shanghai, and Shanghai to Seoul, would the 144 hr transit apply?