You could take I-27 south at Amarillo to Lubbock and US 84 down to I-20. I believe US 84 is 4 lane divided all the way.
And if it were me, I would just stay on I-20 around the southwest corner of Ft Worth to I-35W south to Alvarado. And do it mid day. That short stretch of I-20 in the FT Worth area should not pose a problem for you. Texas, for the most part, has very good highways. And there are routes avoiding the Ft Worth area entirely. But for those few miles, I would just grin and bear it. You will not be close to Dallas.