Beijing Visa-Free: Booking Flights Separately

So, I plan to go to Beijing from Nagoya, Japan and take advantage of the 72 hour free period, as well as going to a third (as-yet-undecided) place in Asia.

However it seems to be cheaper to buy my Nagoya-Beijing flights first, with about 8 days between the two legs. Then, in the middle of this time, I'll fly to a third place, stay there for a while and come back to Beijing a day or so before the return Japan flight.

Would this be okay? As my Nagoya-Beijing flight ticket would show a duration of about eight days, longer than the free period. However, I'd have another plane ticket, booked separately, showing me leaving the country and coming back.

Would I be able to do this? And would I qualify for the free period both times (as long as both times in Beijing were within the limit)?