I agree, Spktyr, that America's government, as it has evolved, has serious constitutional flaws that can never be undone. One of the ways I would change a New Texas is to change voting rights.
If you weren't living in Texas before the break, you can apply for citizenship but you can't vote for five years. That prevents itinerants from flooding in when they have no intention of staying. We may also have to enact a snowbird law for those living mostly up north except in winter.
The other thing I would suggest is weighting a person's vote based on whether they own land in Texas and whether they own a business in Texas. If you own neither, your vote still counts. But if you own land (including your homestead), your voting strength doubles. If you own a business, it also doubles. If you own both, it triples. This gives a greater say to those who have invested the most in Texas and are the least likely to leave. I might also extend this to soldiers who have served either in the Texas military or the U.S. military.
I know there will be some people who will have a problem with that but, if not enacted, Texas will doom itself to repeating Washington's mistake of becoming a freeloaderocracy. I want the vote to rest in the hands of the people who have committed to make Texas their home and demonstrated that with their time and investment. That's not a liberal-conservative thing. That's a stability thing.
Robert Heinlein had an even better and simpler idea.
Only retired military (and retired long-term non-elected civil servants) would be allowed to vote. These being the only people who have demonstrated that they are willing and able to put the welfare of the country ahead of the welfare of their tribe, family, or selves.
This class would also be the only people allowed to be teachers, policemen, judges or elected officials among a few other ‘protected’ jobs.
Everyone else would be a resident or non-voting citizen.