144 hour visa from USA to china, back to USA.

No, your itinerary is not eligible for 144 hour visa free transit for one reason... You are not allowed to travel from one to the other transit area (Beijing to Shanghai) as you have suggested in your itinerary or simply speaking you are not allowed to have two mainland Chinese points in a row if you want to enjoy 144 hour visa free transit.

So, you can fly from US to Beijing, but you have to take a nonstop flight from Beijing to Hong Kong and bypass Shanghai.

If Shanghai is on your visit list you can be creative and fly from US to Beijing, then from Beijing to, for example, South Korea or Taiwan and from there to Shanghai and then to Hong Kong. Like this, you will be able to enjoy 144 hour visa free transit in both Beijing and Shanghai.