I'd love to help, depending upon the weather and the schedule. Unfortunately, I have obligations Sat., 10/19, and I'm already flying a transport on Sun., 10/20.
Have you tried searching for pilots along the route and emailing/private messaging them? I know there is a pilot in Austin, one in Mansfield LA (near Shreveport) and a prolific PNP pilot in the Memphis area. I'm kind of out of the way off a direct route, but:
If Roxy could catch transport (air or ground) to near Pearland Regional Airport (LVJ) one day. I could pick her up and board her at my vet overnight (they do it for free for me). Then I'd pick up up at 8 a.m. next day to fly to Shreveport LA, Vicksburg MS, maybe even further north in MS or in AR, if we can find a connecting pilot. If the Austin-Houston transport is a problem, I could pick her up one day and fly her back for overnight boarding at my vet, then fly one of those legs the next day.
With a little notice (and decent weather), my schedule is flexible enough right now that I can fly just about any day of the week.
Feel free to email me: email@example.com