trigger attribute AJAX using custom select element
I had the same problem and I managed to find the solution. 

You need to call .attr and .trigger

    $('ul.choose-product-quantity li').click(function(){
      var quantity = $(this).children('.product-quantity').text();        
      $('.form-item-attributes-field-product-qty input')
      .filter(function(index){
        return $(this).attr("value") == quantity; 
      })
      .attr('checked', 'checked').trigger('change');
    });


See attached screenshot as well. Good luck. !

Custom attributes selector (image)