UH doesn't take many transfers. UT is actually one of those schools that will look at your pre-LS numbers, although they're more lax with Texas residents. I believe they state this on their website; for that matter, most schools clearly state their transfer admission policies on their websites.
I'd apply to SMU if I were you. Great job prospects, some say as good as UT in DFW. I'd also apply to Baylor, although I don't know anything about their transfer policies. Tech is definitely a rung below those two, although you'd be better off there than you are now.
Some Tulane grads end up in Houston. For some reason, Tulane seems to take a fair amount of transfers, and it's sort of a name-brand school.
If you're more free about where you want to live, try applying to WUSTL. They take a lot of transfers too.