using 72hrs visa exemption 2 continous times

hello,

i cannot apply for normal tourist L type entry permit for China due to lack of time before my trip.
As I would love to visit Beijing, i am planning to do this:

Amsterdam to Taipei
Taipei to Beijing and use the 72 hrs free transit
Beijing to Hong Kong
next day Hong Kong back to Beijing and use the 72 hrs free transit for the second time
Beijing to Amsterdam

can I do this?

I read I will get a stamp in my passport at the Beijing airport saying the duration of my 72 hrs transit permit exemption, if I leave in time, and the next day I am back to Beijing again asking again for the 72 hrs exemption, will I get it? Will I have a problem at the airport?

In both cases I will have proof of my air ticket reservation to leave Beijing in the next 72 hrs.

Please advise.