Can I move the zoom and navigation buttons around?

You can move the navigation and zoom around by applying CSS to their holder divs:
map_outer, map_zoom, map_legend
and using the !important attribute to override the defaults.   So, you can move the navigation arrows to the right by adding this to the map when you embed:
  #map_outer{left: auto !important; right: 3px; bottom: auto; top: 0px; !important;}
  #map_zoom{bottom: auto; top: 40px !important; right: 3px; left: auto !important;}

The result: