A partial answer.
In 2014, we flew London - Paris - Beijing with Air France, spent a few days in Beijing, and flew on to Manila with Philippine Airlines. The tickets were not just with different airlines but bought separately. We had no visa problems.
A few weeks later, we went home on the reverse trip and again stopped in Beijing.
This answer is not quite perfect for you since we had single entry visas which we used on the way out so that we could stay more than 72 hours. For the return trip, we did not have a visa and relied on the stop over visa.
One thing to note on the stop over visa is that it is only valid for Beijing. So, for example, you should not go to visit the Great Wall since that is outside Beijing.
We did not stay there 2 weeks and I don't see how you could with your plan. You will have two visits with a maximum of 72 hours with a gap between them. I guess that you could try going in and out multiple times but you may have a problem. This sort of visa dodging is disliked by many countries and, I think, the 72 hour visa does not allow you return to where you came from.
Why not get a visa? It is a bit slow and expensive but I would expect still less hassle and cheaper than trying to get around it with complex travel plans.