It would add about 65 miles over the direct route to go to Clarksville by way of Little Rock, but that is the only way I can see that would not involve some very crooked roads.
BTW, I would probably choose the crooked roads myself. In fact we did in November when we went up to Dardanelle State Park at Russellville. But there is no doubt these are some of the crookedest roads we've traveled.
Likewise to go to Beaver Dam Site via Alma(Ft. Smith) would add about 40 miles to the trip from Clarksville. But the I-540 is a great highway to Fayetteville/Springdale.
Maybe someone else might have different ideas, but these are my honest opinions. Yes, I would probably go the more direct route, take my time, and enjoy it. But crooked that would be.