I have to echo Dirigo in that, based on what you've said, you may have "overthought" going to law school, but you have not over-researched. Things aren't as black and white as most of the comments on here, but they're also not far off, either.
If your GPA were 3.8-ish you would have a decent shot at UH and SMU, but much less so in the 3.5 range. I don't really trust sites that rely on a small sample of students who self-report results, but most schools list their actual admits in ranges on LSAC.org. Tulane lists your numbers as "Possible"; not a word that would make me confident. For UH, in 2013 they only admitted 6 students with 150-154 and 3.25-3.49 out of 111 applicants. Even TAMU might not be the slam dunk it appears. They jumped 2 pts. this year to 154, leaving you below their median now. I think your chances are still good (better than 50%), but you never know.
For statistical purposes, all "H's" (even Cubans, and all other minorities for that matter) "count". I.e. all the % minority stats you see include Cubans, whether or not they are considered underrepresented or not. Whether or not that's enough for a school to give you a bump will depend on the school. In Texas, it's not like UH is hurting for Hispanic students and unless you come from South Florida or were actually born in Cuba, a school might not really see you as bringing something distinct to the table.
I agree that the prudent thing to do would be to work out in the real world for at least a year while you REALLY study for the LSAT. Like, at least six months of consistent, 4+ days a week study. Working is never a waste of time. It's not like you're 50 years old with kids and a limited window left to your working years. One or two years now will make you still young when you finish law school, but could drastically alter the trajectory of your professional career if it results in better law school prospects. If it doesn't, the worst case is that you gained some real-world experience, saved some money, and come up with a better answer as to why you want to become a lawyer. There is pretty much no downside to waiting.
If you haven't yet, go talk to Karen Severn in the prelaw advising office. Despite TLS's general opinion on prelaw advisers, she's been at this a long time and knows her stuff. She won't BS you.
Texas Tech Law