The only accurate description in my opinion.
Also acceptable in my mind.
That works for Texas as a whole. Really, Texas is Three States. Big Bend, from the coast to El Paso is a lot like the Southwest. The panhandle (and down into the border of Austin) is the "Southern Planes" and the rest of Texas is the south.
Although, Dallas is pretty conservative for such a big city. I wonder why. Also Houston. Totally bucks demographic tradition. Then again, just could be a lot of self-interested rich people and people who don't realise that they're poor. Then again, that's typical of the South and de-centralized "cult towns".
Actually, Dallas is a pretty liberal city. It goes quite heavily Democratic in most elections. It is far more liberal than other big cities near it, say, Houston or Oklahoma City or San Antonio.
I consider Texas to be Texas, but I also consider everything west of the I-35 Corridor (west of I-35W in Fort Worth) to be the Southwest, while everything east of I-35 and I-35E to be Southeast. As far as the Dallas-Fort Worth Metroplex where I live, it is both and neither at the same time. It is Texas.
Oklahoma is even more in question of which geographical region it lies in, because from I-35 west, it is Southwest, from I-35 East and I-40 South, It is Southeast. From I-35 East and I-40 North, it is Midwest. It is also in the Southern Plains from US-412 (Woodward-Enid-Tulsa) and points south and the Central Plains from US-412 and points north to I-80 in Southern Nebraska. The panhandle out east toward Alva in eastern Woods County is High Plains. The Ozarks begin around Vinita, Oklahoma (I-44 halfway between Tulsa and Joplin) and go all the way up toward St Louis, Missouri.
Both Oklahoma and Texas have an identity crisis in terms of where it lies. Really, Kansas has that same id crisis, too.