We often go through Caruthersville on our way to Kentucky. I'm sure you know that the direct route to Texas would be south on I-55 then I-40 to Little Rock and I-30 on to Texarkana.
On that route you could still stop at Maumelle Park near Little Rock. It is one of the nicest public parks we've ever stayed in. That would be just 225 miles from Caruthersville.
Another 260 miles would put you into Tyler State Park near Tyler, Texas. In fact you'd have several choices in this part of East Texas: Caddo Lake State Park is unique, also Daingerfield State Park.
If you want to get off the freeway you could continue on I-155 onto US 412 into Walnut Ridge or Jonesboro, Arkansas and pick up (for example) US 67. We have followed this route a couple of time. We have stayed at Jacksonport State Park (off US 67) and Wolley Hollow State Park in Arkansas. If you want to really take your time, a nice stop would be Petit Jean State Park in Arkansas.
These are just some observations that come to mind. Lots of possible variations.
