It all started in Florida about a decade ago when a family of explorers started on a quest to find the most remote spot in all of the lower 48. To date they have successfully categorized the most remote spot in a total of 38 states.
The most remote spot in Missouri is located in the Mark Twain National Forest in a region south of Springfield. In total it is a 3 hour one-way hike on Long Creek Trail. It’s about a 4 hour drive from KC to reach the trail head.
They have documented all of the trips and have a stat sheet with some interesting information on their website. You can find all of the stats on the Missouri trip here.