Can I add a separate flight to make this work?

Right now I have tickets going from Utah to Japan to Shanghai, and then flying out of Beijing back to Utah. I had planned to fly into Shanghai in the morning of the 8th, stay until we took a train to Beijing on the 10th and then fly back to Utah on the 12th. I thought I could go by using free transit, but it looks like going from Shanghai to Beijing will prevent me from using the 144 hr free transit rule, right? I can stay longer in Japan, or somewhere else, and skip Shanghai, but I don't want to lose my return trip to Utah from Beijing since it would be so expensive to replace. So I'm trying to figure out how to get to Beijing for my flight, without getting a visa this close to my trip. Could I go to Beijing on the 72 hr rule if I got a new one way ticket from Japan to Beijing (and just skipped Shanghai all together)? Or could I get 2 day flight from Shanghai to Hong Kong to Beijing, and that would fix the problem?