Ditch the tortillas, red bans, and rice . Ain't you Texans the ones who invented the beanless chilli? I make tex mex all the time with beef and veggies (less rice and beans makes room for more delicious beef IMO)....just down it all with a fork.
Oh, and some corn tortillas once in a while are not as bad as the floured tortillas at least. Legumes, if done right, are also a grey area where you could throw em in once in a while.