If Missouri is anything like neighboring Arkansas, there will be gas stations with sandwich counters, and they'll have deli meats, in almost every small town. The more remote the town, the more likely they can make you a ham and cheese on white bread with Miracle Whip. You could pick up a piece of fried chicken for later as you're passing through a bigger town on your route.
I've had really good food at small town diners, but then I have really low standards for cheeseburgers and fries. 
Karen
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insidious ungovernable cardboard