There are 2 options to avoid I-40 construction between Little Rock and West Memphis (eastern half of the state).
Option 1 is US 70 which closely parallels I-40 and generally is only a few miles south of the interstate, but generally goes through small towns without bypasses.
Option 2 is US 64 which is 10-20 miles north of the interstate from Marion (5 miles north of West Memphis on I-55) through Wynne, Bald Knob, then combines going southwest with US 67 from Searcy to Beebe (divided 4 lane), and US 64 west from Beebe to Conway to rejoin I-40. Most towns are bypassed, and US 64 particularly has periodic alternating 3 lane sections for passing. MapQuest quotes 10 miles less distance Marion to Conway, but 10 minutes longer travel time.