If a trial court favors a habeas app'n on the "Kentucky v. Padilla" basis, do we have any kind of post-hearing remedy if the accused suceeded but we objected on the basis that he did not carry his habeas burden of proof?

Was it an art. 11.072 probation writ? If so, you can take a State's appeal. If it is an 11.07 writ, the Court of Criminal Appeals makes the ultimate ruling.

Likely talking about a writ application for a misdemeanor. Yes, you can take an appeal to the court of appeals.