Tried a lot of approaches, both complicated and simple ones, but the answer was so straight-forward when I finally achieved it, that I felt kinda dumb for not thinking of it earlier

Just swap your code with this on your map movieclip:

Actionscript Code:
on(press){
    startDrag(this, false, 0, 0, Stage.width-this._width, Stage.height-this._height);
}

on(release, releaseOutside){
    stopDrag();
}

Hope this works