You're missing the big picture. On the Texas Supreme Court, he had no opportunity to reinterpret the Constitution. He was bound by the Supreme Court's decisions. If he had an abortion case before him, he had to apply Roe. It's as simple as that.
It has nothing to do with how he would rule if he was on the Supreme Court. In order to know that, you need to know his personal views. And you aren't going to learn his personal views by reading his cases. Those only apply the law as it is handed down by the Supreme Court.
Let me remind you that prior GOP Presidents appointed O'Connor, Souter, Kennedy, and Stevens, thinking they were conservatives based on their records. They turned out to be liberals.
But based on her speeches, we can be quite sure that Brown is a reliable constructionist, that's for sure.