CLT

The LHR-CLT flight leaves at 9:55pm with at 2:10pm arrival; LHR-PHL departs at 12:05 and arrives at 3:30pm.

Both flights to SAT from CLT and PHL leave after 6pm. Even during off season customs at PHL can be a zoo in the afternoon as most of the international arrivals come in between 2 and 5.

You would also have some other additional flights to get you into SAT with an additional connection, if you misconnect in either airport.