Well it was less “being paid for delivery” and “a bet being made to bait them into getting arrested for bootlegging”. The Burdettes seemed like the “we have so much money let’s see what we can make people try to do” crowd.
Also, I don’t think all of Interstate 20 was finished by time the movie came out, there were parts that did not open until the late 70s.
And a major plot point was the national speed limit of 55 being introduced, and the ruthlessness some states enforced that, specially on truckers (A similar idea expressed in the movie Convoy). Also truckers, legally can’t just drive for 20 hours straight with minimal time off for food and so forth. (This was also around the time that more limits were put on how long they could be on duty and how strict log keeping was going to be viewed)
So between segments of I-20 not being done yet, a strictly enforced 55 limit, and limits to how long you can be “on duty” as a driver, that would all add time to the round trip.