Years ago (1997), we made a long trip and bagged six southern highpoints (MS, AL, FL, GA, SC, TN). It was also our family vacation to Disney World and other FL attractions, hence the two-week timeline. You can easily do the Konvention plus four to six highpoints in a week. 1997 trip report
is on my web site
. (No, Nathan doesn't look much like that any more. He's 6'2", 21 years old and over in Munich doing junior year abroad from Northwestern University. Time flies when you're having fun!)
Keep in mind that it's a pretty fur piece out to the AR highpoint. Plus, you'll be on state (two-lane) roads nearly all the time between MO and AR if you try to take the direct route. Pretty parts of both states, though, through the Ozark Mountains (hills). LA is close to the Interstate but both MO and AR are out in the country.
If you have any questions about MO, yell...that's my home state and I'm happy to help with directions and suggestions.