Well we always take I-10 to I-49 that north to Shreveport and take the bypass around that city to US 71 N to US 82. Follow 82 until it hits US 287. Take 287 into thru Amarillo and a bit north to US 87 W. Follow that to I-25. That avoids Dallas/Ft Worth, Houston and Oklahoma City all of which are a PITA to drive thru.
This is a good route, in my opinion. An alternative is to continue on I-20 from Shreveport to US 69 (near Tyler) up to US 82 and then as above. Both routes avoid DFW altogether and are far better now than taking US 180 west from Greenville (from I-30) with all the traffic signals and congestions north of Dallas.
So the essential is US 82 to US 287 and US 87 to I-25. We just made this route less than a week ago.