You could give the link an onClick handler:

<a href="#" onClick="load()">Your link</a>

and then add script to the page with the link:

<script language="javascript">
function load()
{
 var newwin = window.open("the_processing_request_page.htm","new win","//window attributes...");
 window.location = "the_new_page.htm";
}

Give the new page (the one you have been waiting for to load) this code:

<script language="javascript">
var newwin = window.open("the_processing_request_page.htm","new win","//the same window attributes...");
newwin.window.close();
</script>

The new page should still recognize the popup and close it.

Sorry, I don't know how to make different messages closer to when the page is finished loading.

Hope it helps!