After spending a significant amount of time searching on Google for a solution to my issue, I decided to change my approach. I implemented the following scenario and it worked flawlessly for me:
$j("#shipping_method optgroup[label='Free Shipping']").clone("optgroup[label='Free Shipping']").insertAfter("#shipping_method_form");
$j("#shipping_method optgroup[label='Free Shipping']").remove();
$j(".box-content .fedex").appendTo("#shipping_method");
#shipping_method_form is the id of my select box
The above example is from my experience. Feel free to take a look and hopefully this can provide a better solution for all browsers.