Scoring above 1400 on the SAT and taking AP courses in itself is not enough to get into UT engineering or CS. You just described a mediocre Asian kid. I should know, I'm Asian. These two programs are top 10 in the nation. UT is big on the concept of 'fit to major'. They want to see that your high school coursework align with your major. My son got into UT CS last fall. Knowing how difficult it was to get into CS at UT, we loaded his high school coursework with advanced CS classes, robotics, and engineering. He was also top 6% in his class (#4 overall). I do believe this was why he got accepted. I was still not sure if this was going to be enough. He has a friend just got into UT engineering (electrical). She is Asian and scored above 1500 on her SAT and is a 4-year All-State violinist and is the salutatorian of her high school. Moral of the story is that there are a lot of different criteria that UT uses for admissions. The talent of the applicants applying for these programs are off the charts. It's not only what you are doing but how do you stack up against other kids.
I'm also for affirmative action. I will take the poor kid that did well in school that did not have endless resources to take SAT prep classes, private schools, etc. This shows a ton of character and will. These are just as important criteria for admission as standardized test scores.