London-Shanghai-Tokyo followed by Tokyo-Shanghai-London

Jason, your itineraries are definitely eligible for 240 hour visa free transit - twice. It is definitely allowed to use this particular visa free transit scheme twice within a very short time frame. Also, during your stay in China, you are allowed to travel within the major part (although not all) of the country because the old transit zones and the limiting of movements between them were scraped. In other words, you can even travel from Shanghai to Xi'an and after that to return from there back to Shanghai. Consequently, you are free to travel and to stay in Nanjing without any doubt. Have a nice journey.