South Korea to Beijing, via which to Canada

Hi,
I'm an ESL teacher in South Korea, but my contract in South Korea is ending in March. My boss has booked me two separate flight tickets because it was cheaper that way. I am supposed to take a night flight on Monday to PEK and my next flight isn't until Wednesday evening to go to Canada. Since they are two separate bookings I am worried that I won't qualify for the 72 hour Transit Visa. I can't get a regular visa because you need to have 6 months left on your alien registration card, which I don't. Will I be able to get the 72 hour transit visa at the airport in PEK even though I don't have a connecting flight, it's a separate booking. Please help! Thank you!