Well, now you're dodging the spirit of the problem, which was to work through a single generalization of "map" (or, as tweaked in the second try, "map_unless_test") that is responsible for executing the callback and collecting the results into a new array. Here you are doing the result-collection on your own. You can't express these functions elegantly if you are required to silo the .push(cb(item))-ing into a separate "map" or map-like function.

That's not an outlandish requirement; imagine that the callback can be expensive, and we would like to be able to adjust a centralized "map" function later so it farms things out to different processes/workers/etc.

To solve this for map_first_innermost, you'd have to throw an exception with the nested array, but this is just getting hideously ugly.

  function map_first_innermost(arr, callback) {
    try {
      return map(arr, function(v) { 
        if (v instanceof Array) throw {itWasNested: v}; 
        return callback(v);
      });
    } catch (e) {
      if (e.itWasNested) { 
        return map_first_innermost(e.itWasNested, callback); 
      }
      throw e;
    }
  }