It's been years ago that I hunted it, but you'll definitely have room to stretch your legs and wear out some shoe leather. You might take a look at the Missouri Department of Conservation site for detailed harvest summaries by county to narrow your search. There are some huge continuous tracts but if there's good road access can also be lots of pressure, spooky hush-mouthed birds, and bumbling hunters ruining your setups.
I've known lots of folks that floated via canoe to reach places that allowed great hunting of totally unmolested birds. LOTS of floatable rivers through the MTNF: Big Piney, Eleven Point, Black, and Current to name a very few.