I'm not from texas but I can guess that the sun there gets very hot on the new leaves of your tree, Maybe you should put up some sort of shade over the tree until the new tree is stong enough and roots are well established in it's new home.

Thank you terry for your suggestion. Yes our sun is very hot! lol. I rigged up a little shade with some cheesecloth for today. I will find something better tomorrow. Hope this is the answer.

I am in Lake Jackson, TX and I can't put any of my Bordeaux family figs in the full sun. Yes yours is in that family. I had one even where it got 2 hours of late afternoon sun and almost lost it. I have moved them all to a morning sun only area and they are starting to take off.
I think it's just too intense down here compared to other parts of the country.

Of course is too intense and shade in the afternoon is the answer,for certain varieties.
If I was you I will try late ripening varieties,and Mount Etna type for Early,+ Malta Black,and Lsu Cultivars.