(Also new to me: the hillside theater at Zilker Park, which was very nice, especially with the addition of a little picnic basket.)
This version was set in 1890s Texas (more or less), with all the place names changed. So in the original, where a traveler says his trip will take him
...as far as Rome;in this version, the traveler says that he's going to Dallas or Abilene or Fredericksburg. I can't remember which, which shows that that sort of info is easily swapped out. You could place this on a spaceship or in modern day New York and easily replace the place names without changing much about the play.
And so to Tripoli, if God lend me life
What you can't replace is the central plot, about Petruchio crushing Katherine's spirit by starving her, disrupting her sleep schedule, dressing her in his clothes, and teasing her with beautiful new clothes that he won't let her have. Or some combination of tactics that may remind you of standard cult activity. (Or standard activity at a military bootcamp, or Gitmo, or... Lots of organizations like to break people's spirit.)
(Well, teasing someone with clothes that they can't have is perhaps a little more specific; but in general, offering/teasing people with some reward is pretty standard.)
There's a lot of argument about the meaning of this plot. Is Shakespeare advocating it? Is he making fun of it? Is it about more than gender?
But however you take it, seeing a man torture a woman into submission is a little offputting.
(I remember going to see Who's Afraid of Virginia Woolf? at the University of Chicago Theater; and I remember the sound of the entire audience catching its breath when we remembered that this play was about a viciously unhappy couple in academia. I felt a similar moment at the theater when Petruchio starts starving his wife.)
Maybe it's just that I recently watched Unbreakable Kimmy Schmidt that has me thinking about things this way, but I'm wondering what's a way to play Taming of the Shrew and be smart about this plot? Perhaps you could rewrite it literally as the story of a cult...