I would take US45 to Jackson, TN then US412 to Dyersburg, TN then I155/US412 to Kennett, MO stay on 412 to Walnut Ridge, AR then pickup US62 South to Beebe, AR then US64 to Conway, AR then get on I40 West. Here is a link to Arkansas High Dept. Road construction I40 West from Memphis has some construction down to 1 lane and the have lots of accidents that bring traffic to a total stop. The way I said to go is the way all the oversize loads go because of the construction on I40 between Memphis and Little Rock. http://www.idrivearkansas.com/#traffic These are good roads and not a lot of traffic.
