Transit between airports in Shanghai

No, unfortunately, this is not allowed. When somebody travels through China on 144 hour visa free transit, she/he is allowed to have just a landing within one transit area. In simple words, you cannot have two mainland Chinese landings in a row. This is allowed only when traveling on 24 hour visa free transit and that means that you have to accomplish your entire transit time in mainland China, counting from your first scheduled landing, until your last scheduled departure, within 24 hours time frame.

To conclude, in order to avoid the need of issuing of the Chinese visa in advance, you should alter your flight itinerary to have just one mainland Chinese destination (landing) or to accomplish your originally planned itinerary within 24 hour time frame. If you remain with your original itinerary, you will have to obtain a Chinese visa in advance. I'm sorry.