Missouri Native here. Born and raised in the St. Louis area. Spent all my summers growing up at the Lake of the Ozarks. Attended college North of Kansas City. My job and kids in college require me to drive around the state frequently. So, I'm pretty familiar with these areas. Here's some perspective that may help.
The Lamine River flows North/Northeast from Central Missouri, into the Missouri River just west of Boonville, MO. Boonville is just to the west on Interstate 70 from Columbia, MO.
The Gasconade River flows North/Northeast from South Central Missouri, into the Missouri River just west of Hermann, MO.
Boonville to Hermann is 88 Miles or 1 hour 22 minutes.
Columbia to Hermann is 80.6 Miles or 1 hour 16 minutes.
The most logical routes (Boonville to Columbia to Hermann) would take I-70 East to County Highway 19 South into Hermann.
(edited: spelling)