144 hour visa.Thanks

I have a round the world trip booked from

NZL - CHNA
CHINA - FRANKFURT
LONDON - USA
USA - NZL

I will be landing in Beijing capital.
I will be in Beijing for just over 3 days (80 hours)
I also have a New Zealand passort.

Do i qualify for the 144 hour exemption with these flights?

Also how do I approach the airline about the 144hour free transit exemption as it seems that a lot of airlines are unaware of this exemption and sometimes deny travelers from boarding without entry permit.