Well Southwestern was formed from the merger of several struggling Methodist schools. The oldest of those was chartered in 1840, but it got a new charter from the state in 1875. Austin College was chartered in 1849, and has been operating under that same charter ever since. They did merge with Texas Presbyterian, an all girls school, in 1930. Thus Austin College has been continuously operating under the same charter longer than in other college or university. They were also the first college in Texas to grant a graduate degree. Today they only grant Master's degrees in Education. They did change locations, from Huntsville to Sherman in 1876, for much the same reasons that the schools which made up Southwestern chose to merge at Georgetown. Yellow Fever was a real problem at the original location(s) and the schools all suffered in the aftermath of the War of Yankee Aggression.
Baylor was originally chartered in 1845, but didn't confer their first degree until 1854. In 1886 they consolidated with Waco College, which was under control of a different Baptist group beginning in 1847, and a new charter was issued as Baylor University at Waco (The original Baylor had been at Independence) in 1886.
So, Southwestern has the oldest roots, Baylor's roots go back farther than Austin College's, but Austin College has been operating under the same charter the longest, in fact since it's original founding.
The site in Huntsville where they were originally located is now the site of Sam Houston State, having passed through the hands of a short lived Methodist school. When the last remaining former Austin College building burned down some years ago, some of the timbers were salvaged and a ceremonial "Mace" constructed of one of them was presented to Austin College by Sam Houston (or it's students). That Mace leads the procession at Graduation and other important events at AC, along with 2 to 4 pipers in keeping with the school's Presbyterian roots. It's an impressive beastie. :)
You did quite a bit of research! Thank you for all the history, and I'll pass it on to my daughter. She is very happy at SWU (freshman). I was so impressed with SWU, Austin, and Trinity. All three are top notch, and she wanted a smaller school. I'd have been thrilled with whichever one she chose.We are in the Waco area, but she refused to consider Baylor even though many of her friends chose to go there -- the "too close to home" syndrome for her.