I live in Tulsa and would be happy to help you out of Tulsa. I would strongly suggest you look at the Arkansas Bike Suitability map and see if you want to ride northern Arkansas. If you do, I highly recommend you not ride west of Fayetteville to Harrison during a weekend as the traffic is worse.
If you do a central AR route across AR (Ft. Smith area to Memphis) I can help you with a route.
Both AR & OK have lots of semi-narrow highways with no shoulders. AR makes it worse with lots of curves and hills. Beautiful state to ride through though.
If you want help, contact me privately.