Coming from someone that travels most of that route...
I40 to Tucumcari, NM... pick up Route 54. Follow Route 54 to I-135N. Take I-135 north to Route 50. Follow Route 50 to I-35 (this jog bypasses the tollroad). Run I-35 to I-470E/N. Follow i-470E/N to I-40E and head for St. Louis... this is THE quickest way to St. Louis.
I run that route about every 3 months... cuts off a lot of time even though it is 2-lane roads... and there are lots of diesel stops along Route 54, and a Flying J at the intersection of Route 50 and I-35. And these are mostly roads in good condition...
I personally hate I-44 in MO... windy, twisty, rough. I-40 to Memphis (to I-55) is a long ride too. And I-40 to I-35... well, my route cuts that corner off.
I try to avoid TX since it has that new speedlimit and everyone races along at 85mph or more...
steved