I know you’ve already traveled, but for anyone else with the same question in the future, I’d like to give an answer.
Beijing is huge and the Beijing Capital Airport is located on the north-east side of town. Tianjin is just 100 km east of the Airport; about 1.5 hours by taxi.
Beijing south railway station is on the opposite side of Beijing; to go there you will be traveling through the center of a huge busy city.
From the Beijing airport to Beijing South Railway station, it will be about an hour by taxi. You will need to get to Beijing south at least an hour before the train leaves to get tickets and wait and board. It will take 30 minutes to ride the train to Tianjin. It will then be 30+ minutes to your hotel. That’s at least 2.5 hours – with no hijinks.
Why not just go directly to to Tianjin? I agree that the intercity high-speed rail is interesting, but it might be prudent to rest a bit from the flight before hustling through the railway stations as an illiterate foreigner. It is really fun, but better after a shower and a good nights rest.
Cost-wise, it will also probably be comparable. The taxi is far easier.
Edit: mts has found a source that shows a cost of about 500 yuan for the taxi directly to Tianjin, and a cost of about 250 yuan for a pure-train/subway/high speed train transit method. This means for two people, the price is the same.
The question considers a taxi to Beijing South Railway Station; this will push the cost benefit analysis in even more favor for the direct taxi option, even for a single person.
mts also suggest this SE link about uber. In my experience in China, uber is about half the price of taxis; although I prefer metered taxis for personal reasons.
This is an incomplete answer as unfortunately I have no experience about the BeiJing – TianJin connection.
In general your considerations seem sensible to me, here are some remarks though:
Credit:stackoverflow.com‘