Don't think Texas, think distance. Most or all of 4 other states are closer to Dallas than Big Bend is (as you know).

I was disapointed with Davey Crocket NF, it's pretty crowded and it seems as though you're never out of hearing range of a dirt road with lots of pickup truck traffic. Maybe I just caught it at a bad time.

From Dallas you're not much more than 2 or 3 hours from Talimena SP in OK. You can park there, hike and camp on the Ouachita Trail, and use their shower before driving home. I really like a loop that includes Military Road, a well-built trail with interesting history.

Broken Bow is smaller but a little closer, we enjoyed a quick trip there a few years back.