An first attempt to make a 100% client side web part know that it's being edited.

dynamic_webpart.js

(function() { 
  var $wrappingDiv = $('div[webpartid]').last();
  //console.log($wrappingDiv.attr('webpartid'));

  $(document).ready(function() {
    var inDesignMode = null;
    if($('#MSOLayout_InDesignMode')) {
      inDesignMode = $('#MSOLayout_InDesignMode').val();
    }

    var wikiInEditMode = null; 
    if(typeof document.forms[MSOWebPartPageFormName]._wikiPageMode !== "undefined") {
      wikiInEditMode = document.forms[MSOWebPartPageFormName]._wikiPageMode.value;
    }

    if (inDesignMode === "1" || wikiInEditMode === "Edit" || $('div[webpartid][selectedwebpart="true"]'))
    {
      // page is in edit mode
      //console.log('edit mode');
      if($('div[webpartid][selectedwebpart="true"]')) {
        if($('div[webpartid][selectedwebpart="true"]').attr('webpartid') === $wrappingDiv.attr('webpartid')) {
          console.log("EDITING OUR WEBPART!!!");
        };
      }
      //.ms-WPSelected ?
    }
    else
    {
      // page is in browse mode
      console.log('browse mode');
    }
  });
}());

Need to attach some type of init() handler to a global object with the current webpartid and ensure our .ready() is only called once. When ready fires it should do a lookup into the global object to see if there is a handler to be called.