I arrive at 5 am, and have a flight departing at 8 am. I will be arriving in Bejing with two suitcases that I don't need in my next city, and want to ship to a hotel in Southern China.

I happen to know that there are post offices at T2 and T3.
Terminal 2: Opposite to Gate No.2 of the Departure Hall
Terminal 3: East of the hall on the F1
Their service hours are from 07:00 to 20:00, so you may be able to succeed in shipping your luggage there.
Good luck~