No shortage of hilly/curvy roads in northern AR.
If you like driving 'hilly/curvy roads', look at the road between Mountain Home and Melbourne AR. I drove it in a blinding rainstorm right on dusk, some years ago when I was heading west out of Melbourne. Now that was a challenge. I imagine it would be a wonderful drive in fine weather.
Have a great trip.
Lifey
Pig Trail and Other Scenic Byways
There are, in fact, any number of great scenic routes through the Ozarks and other 'mountains' of Arkansas. None of them, however, go through Little Rock. In any event, 350 miles is a bit much to try to do after work on a Friday evening, so your goal for that day should just be to get yourself into position to start the scenic driving the next day after a good night's sleep. If you were to get even to the Texarkana area, a much more manageable 200 miles from Fort Worth, on Friday then you could have yourself a great Saturday and early Sunday, finishing up on Sunday early afternoon within reasonable distance of getting home by bedtime.
So what roads could you string together on Saturday and Sunday? Start with US-71 north out of Texarkana, a relatively scenic road in its own right it will serve as the main connecting route for the other more 'back roads' scenic byways such as the Pig Trail (AR-23 in northwestern Arkansas), the roughly parallel Ozark Highlands Scenic Byway (AR-21), the Mount Magazine Scenic Byway (AR-309 out of Paris AR and up the mountain), and for the way home the Talimena Scenic Byway westward into Oklahoma.
AZBuck