I'd say make your way down to Springfield and either continue south to US 412 and east to US 63 south or take US 60 from Springfield east to US 63 south. US 412 is a nice ride through northern AR.
I grew up on that highway in east AR. It's somewhat slow going, but not too heavily traveled so traffic shouldn't be a concern. It will take you through some pretty scenery especially around Mountain View if you have the time available.
I did most of that ride about a month ago. I started out in Memphis and went through Joneboro, then into Missouri via Mammoth Springs. I took 142 from Thayer, Mo and finally caught 160 close to Branson. Mostly two lane roads, but there were a lot of great curves and scenery.
AR state brochure, Some good nuggets in here. Avoid I-40 from Little Rock to Memphis. Construction with 1000+ trucks per hour goes from moving to parked very quickly.
here ya go....from south of KC at Harrisonville, take 7 to Clinton on toward Harry S Truman reservoir and hit US65 going South through Springfield , Branson and into Harrison AR. pickup US412 and go East to walnut Ridge. Take US63 from there thru Jonesboro on to Marion and Memphis. You can pickup I55 at Turrell or 63 turns into SH42 into marion on into West Memphis AR....There you have to hit I55 to go south into Memphis and take US 78 out of Memphis into MS to Tupelo and on to Columbus.. The area from Jonesboro toward Memphis Sucks, ain't nothing I can do bout that.....now matter which way you go........Nice once you get out of Memphis area toward Tupelo.....