Missouri to California 2 or 3 times a year as a kid, still caught a lot Old Route 66 when I-40 was still getting patched together ! Have done it a few times in the last decade, and of course , just not the same !
Once you get across West Texas and Oklahoma, the view gets a little better, IMHO ! Probably the most condensed and original, read run-down into that, is the 4-states corner of Oklahoma, Kansas, which is the shortest state stretch on the whole route, and then into Missouri.
As a little jaded as I have become to it, living in the Joplin area for over 25 years, it is absolutely amazing how many International car clubs, historic and antique car rallies and runs, and motorcycle tours work the heck out of that route !
Add to that your timing, with the weather still decent, and you could really get an eye full of who knows what ! Sounds like I work for the tourism board ! LOL !
If you want to catch the views, thats my 2 cents worth, otherwise I- 44 parallels it most of the way from OKC to St. Louis and beyond ! And it moves at 75 in Ok., 70 in Mo, it just sneaks by the corner of Kansas !
Have fun with it either way !