For reasons beyond my control, I have data coming back from an external service being formatted as an array of array of string: [[\"string_one\", \"string_two\"]]
>
There is quite a big discrepancy between your target object and the JSON. You could do the mapping manually:
string json = "[[\"string_one\", \"string_two\"]]";
dynamic result = JsonConvert.DeserializeObject(json);
var myObject = new MyObject
{
PropertyOne = result[0][0],
PropertyTwo = result[0][1]
};