How can I "reset" <div> to its original state after it has been modified by JavaScript?

I would clone the element, instead of saving the content. Then use replaceWith to restore it:

var divClone = $("#some_div").clone(); // Do this on $(document).ready(function() { ... })

$("#some_div").html("Yeah all good mate!"); // Change the content temporarily

// Use this command if you want to keep divClone as a copy of "#some_div"
$("#some_div").replaceWith(divClone.clone()); // Restore element with a copy of divClone

// Any changes to "#some_div" after this point will affect the value of divClone
$("#some_div").replaceWith(divClone); // Restore element with divClone itself

You can use the data attribute to save the state rather than a variable

$('#some_div').data('old-state', $('#some_div').html());
$('#some_div').html($('#some_div').data('old-state'));

What you're doing is not optimal. The best solution would be this:

When the form gets successfully submitted, just hide() the FORM element, and show() the message (which is initially hidden). And then, later, just show() the FORM element and hide() the message.