OK. First off, you're dealing with a core-&-Blade technology. Could have been off a cone core or one edge of a block -- comes to the same thing either way. Previous removals were from the broken end (the one in the center having ended in a step) ; the one that detached it from the other end (bulb of percussion remnant remains at the tip). Both edges worked into sidescrapers (going by what I can tell from the pictures). The incurve behind the point may have been (?) backing.
So, made with the same techniques and strategies you'd expect (and hope) to find in a Paleo/Plano context. BUT. One thing I've learned here (from Neanderthal) is that Texas, like Florida, was just as much a different planet in tools as it was in points. From what he's told me, the Jarrell phase of the Early Archaic there was (judging by some of the tools it occasionally produced) either continuing that, or coming up with something very like it.
Your best resources would be the Texas Archaeological Resource Laboratory and Neanderthal for a more nearly definitive answer. If it's worth $70 to you to have an ironclad placement in time, send it to Bill Breckenridge for laser testing/evaluation.
Sorry this isn't more definitive, but at least it's worth what you're paying for it