I've driven from Mobile, Al to Fayetteville, Arkansas many times without problems. US 98W out of Mobile to Hattiesburg, Miss, US 49N to Jackson, Miss, Interstate 20W to Tallulah, LA, US 65N, which changes to I-530 in Pine Bluff, Ark, to I-40W in Little Rock, to I-540N in Ft Smith Ark. This will leave you in Fayetteville, Ar, which is about 70 miles from Branson, Mo. Not sure how far north you're going in Missouri, but this route is all 4-lanes except for the part on US 98 from Mobile to Mississipi State line, and about 60 miles of 2 lane from Tallulah, La to Lake Village, Ark. No low bridges or tunnels. Beware of speed traps around Lake Providence, La, however. Fun travels!!