You may have a better chance of killing a real giant mule deer in the Gaines and surrounding county region of the South Plains. You'll likely have to pay a pretty penny to do it, but there are some LARGE muleys there. It's not very rough to get around either. The caprock region of the panhandle (Briscoe County included) holds some monsters too. Don't think that hunting that country will be any easier than hunting the trans-Pecos mountains though. It won't be. It might even be tougher. That is some ROUGH country.
I grew up hunting the canyons of Swisher and Briscoe counties. A mule deer or aoudad hunt in those canyons is as challenging a hunt as you can find in Texas - especially the part that comes after you shoot something and you need to get it up out of the canyon!
Some pics from my son's mule deer hunt at Caprock Canyons State Park on New Year's Eve weekend a month ago....
Coming down the cap into Quitaque
Sunrise over the Llano Estacado and the Texas State Buffalo Herd
Lunch
Glassing a canyon
Lone doe
Last evening buck
We just had a day and a half to hunt, and the wind blew 40mph on day 2. We saw a HUGE buck on the first evening, right before dark. But he was just across the fence on the neighboring ranch. This smaller buck was the only buck we saw on day 2, so Zach took him. It was his first mule deer, and he really wanted to add a new species to his list.
You can enter drawings through Texas Parks and Wildlife to hunt mule deer in several places, including Caprock Canyons, Palo Duro, and Matador Wildlife Management Area at Paducah. We're going to the Matador in March to hunt hogs. Fun stuff.
The End.