Apply to top 30 schools you're interested in. If you don't get into UT, see if you get scholarships at any of these others (if you think you have a good shot at UT, you likely will). Leave options for yourself for when it's time to decide on a school -- in a few months, if you don't get into UT, you will otherwise probably regret limiting your choices by simply deciding not to pay a few more app fees.
This will give you a good amount of time to balance your reasons for in-state TX schools v. sub-T14 regional elites. You may consider informational interviews with attorneys at Houston firms you're interested in working for. They should be happy to talk with a prospective law student about the firm and law school in general, and should be able to give you an idea of how deep they'll go into a class at a texas T2 for EEs. This is a great excuse to talk to them, as they'll also be a valuable contact later when you want your resume to be brought to the attention of the recruiter.
Otherwise, given the specific nature of your question (EE, Texas market), I think the number of people on this forum able to speak accurately on your particular circumstances and what you should do are very small. Unlike the vast majority of law students, there is not a wealth of data on how deep firms actually go to search out EEs at various schools -- only that it's deeper, and that there's an ever-present rumor that you don't really have to worry.
To reiterate, apply to the T30's, talk to Houston attorneys at attractive firms, and balance whatever additional employment risk you've found out you'll be taking on by going to a T2 vs. the immediate lower debt of a T2, but taking into account scholarships you've received at the T30.
Offhand, I would be inclined to think you'd get a reasonable scholarship at WUSTL, which may or may not be well respected by all Texas firms, but is certainly closer to TX than Vandy, GW, UCLA, USC, et. al., and should have accordingly better placement.