Head-to-head has the biggest advantage because it is the only factor that eliminates virtually every other possible variable.
In a word ... ridiculous. It doesn't usually eliminate home-field advantage (even in the case of the Red River Shootout, UT has the edge because it's played in Dallas; it's neutral in name but only somewhat in fact); it doesn't eliminate injuries, confidence, the streaks, good or bad, either team is on; it doesn't eliminate off-the-field distractions. All that factored in makes head-to-head important, but by no means the only or even always the best criterion for a final decision—as it is not in this case.
And we're back to body of work over a season—in which Oklahoma wins again.
Head-to-head is "inordinate" to you because it defeats your position.
Head-to-head's already been exposed as overrated in determining which team is best over a season ... Hell, sometimes even in the game played. The fact that you're unable to accept that it's important, but not paramount, speaks to your inability to accept gettin' whupped in an argument.

Which is a good point and the best one you've made so far.
I'm so far ahead on points and punches that you're already in the locker room goin', "Is it over. Am I still champ?"

And whom did I pick? Pssst... Oklahoma. The difference is that I am allowing for it to be a much tougher decision than you have.
A clear decision is not necessarily an easy one. I've never said or implied Texas wasn't worthy. Oklahoma's simply proven more.
Think about it, Neroon. Until OU's win over Oklahoma State in Stillwater, I rated Texas over Oklahoma, based on the relative equality of their schedules and the fact that UT beat the Sooners. How freakin' convincing do you believe I think it? They passed UT based on an impressive win—which means Texas is, according to my own poll, within a one-impressive-win striking distance.
Again ... narrow, but clear. Accept it.
Perhaps you thought by "clear" I meant "so widespread it's laughable to discuss." I didn't, and don't believe I've implied that at any point during this discussion. You're certainly welcome to point it out if I have, and I'll apologize for hyperbole.
This is college football, though.

"Sorry, but ... I've seen nothing here to refute or even substantially shake that."
You're speaking more intelligently than you ever ha–
Oh, that's why. Quote me more. You'll seem even smarter.

Bottom line: who should be the Big-12 South rep is just not so clear-cut as you are making it out to be.
Beneath the bottom line: You've interpreted my statement that Oklahoma is a clear-cut choice as an indictment of Texas. It's nothing of the sort.
I originally wrote:
2 – Oklahoma (11-1)
I've stayed with the Longhorns based on head-to-head, but unfortunately that's no longer justified, in that OU has played a more impressive schedule than UT. Whuppin' Cincinnati and Texas Christian, coupled with their run through the Big 12, is enough to put them over the top. This final win over OSU gives the Sooners five quality wins, to only four for Texas. Sorry, Longhorns fans: Oklahoma is the better team, based on what we saw on the field. You've got to hope now that Missouri comes through for you, unlikely though that is.
3 – Texas (11-1)
"But we beat them" is a great argument. It's just not a convincing one, ultimately. It reminds me of the season Notre Dame bitched up a storm when they finished number two to an FSU team they'd edged earlier in the year. Problem was that the Irish had gone out the next week and lost to Boston College. The logic was unassailable: The Seminoles had lost to a great Notre Dame squad, while Holtz's boys had dropped one to a good Eagles crew. Based on the body of work, FSU was the better team. Same principle absolutely applies here.
Note I wrote "put them over the top," not "buries Texas in the Big 12 also-rans graveyard."
If I'm 6' 0" and you're 5' 11", from a distance we look to be the same height. But the closer one gets, the more obvious it is that I'm taller. Same principle between 5' 11" Texas and 6' 0" OU.
Texas deserved to be in the discussion. But this idea that Oklahoma edged them by the barest of margins is frankly laughable. OU's the better team—narrowly, but noticeably.