Hi, not suggest that you change to another train at Tianjin since you just could arrive at Beijing South Railway Station as early as at 08:00. And, the south railway station doesn't have more convenient transportation to T3 than from Beijing Railway Station.

When you arrive at Beijing Railway Station, you'd better hire a cab to drive you to the airport directly. 30 minutes is needed at least! Although there is express subway to the airport but 08:30 is the traffic peak time for the subway. Please note that domestic flights in T3 require passengers to check-in 45 minutes in advance at least!

Just for your reference!

I don't know how long it takes to change train at Tianjin, but I assume I could get to Beijing South by 7:25 or 7:40, which I thought would give me a bit more time?

If I do stay on the train to Beijing, I have been advised that it would probably be safer to get the subways to the airport (maximum one hour), rather than risk a cab getting stuck in traffic at that time of the morning?

Hello, sir. There is another way you can try: When you are getting to arrive in Tianjin, ask the staff in the train if he or she can lead you to the intercity bullet train platform to Beijing South Railway Station without getting out of Tianjin Railway Station and enter again, if can buy the ticket when you get on the train. It was practable and I do not know the regulation now. If you can not catch the train at 7:25 (get to Beijing at 7:55), there is no big difference with arrival Beijing at 8:31 by K28. I suggest you take Subway Line 2 to Dongzhimen to catch airport express train.