Pretty sure you can appeal a JP court eviction ruling to county court at law. That's what I'd do, assuming the JP is not following the Texas Property Code. File the eviction, JP refuses to hear / dismisses / rules against you, appeal to CCL.
It will cost you more money, but you may be able to add those expenses to your judgement. You also may be able to "complain" to the state or do whatever was done to George Boyett when he was reprimanded by the state for making up his own rules.
I dunno, I'm not a lawyer, maybe someone who is will weigh in.