Hi,
As an alternate option, you could take I-65 north to Nashville, I-24 from Nashville to I-57 in Illinois, then north on I-57 to I-64 west at Mt. Vernon, IL through St. Louis to Wentzville, MO. Go north on US 61(mostly 4 lane) to US 36 at Hannibal,Mo. Take US 36 across Missouri to your destination. US 36 is all 4 lane highway.
One other option is to take US 72 west from Huntsville, AL to Corinth, MS then north on US 45 to Dyersburg, TN. Take I-155 from Dyersburg, TN to I-55 north at Hayti, MO. Follow I-55 north to Sikeston, MO. Take US 60 west(4 lane highway) from Sikeston, MO to Springfield, MO. Go north on MO 13 to Hamilton, MO. Hope this helps. Safe travels and enjoy the journey.