Have done some similar trips in my day. Make sure you know the hunting reg's and don't take any game outside them that can land you in trouble with the law.
I typically did a fast thatched hut style 3-sided shelter with a space at the rear to crawl out and a firepit about 3ft away with a reflector. Remember that many such shelters are flammable and plan accordingly. I haven't done this kind of thing in Texas scrub, so that style shelter may not work as well for you. I have seen a few "shows" where in scrub desert they use rocks and fire reflector to keep warm with little building req'd.
Depending on what kind of firearm you take, I'd plan to spend more time seeking clean water and take targets of opportunity during this endeavor. I think a .410 with a few slugs for defense and shot for birds/snakes and small mammals (for food) would allow you to carry the most ammo. I'd say a .22 LR except if you run into a Mountain Lion or blackbear etc, you might need a slug. Anything you do kill, make sure you clean it and leave the viscera well (300 yards+) away from your camp if possible. This might draw predators in and you don't want to bring them on top of you. I personally would probably risk the weight though and bring a 12 ga. I usually carried one .22 rifle and had my Crosman 1377 pump .177 pellet pistol on a leg holster. Most of the small game came from the pellet gun and I saved the .22 for better opportunities.
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If you guys are all carrying different weapons and sticking together, have one bring a .22, one a 12 ga. and one a 30-30 or .45-70. This would give you predator protection, both small and large game taking capability and defense in case of 2 legged issues.
I always make sure I carry a couple magnesium firestarters in my kit. They don't care about wetness and work very well. Mine have saved my toes a few times during falling through ice.
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Finally, make sure you have a good water filtration device. For short term, you might get by with the "biostraw" personal filter concept, but you would each have to have one. You might pick up one good hand-pump style and then share the water. I always keep iodine tablets in my kit also, incase the filter quits working or is broken/lost. You can actually live up to 56 days without food, but 3 without water typically. So energy should go to water finding and food secondarily.
Just some musings. Hope you guys have fun and stay safe. Up here we didn't have puma or bears to worry about.
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