The name/value pair is included in the query string if you submit the form by pressing enter
if you have tabbed to the submit button, which would have to be the case in this application (that, or clicking on the button). Actually, Mozilla always sends the submit button name/value pair - it's IE that doesn't unless the button is clicked or highlighted.
As for a workaround, you have to choose among hacks. There's the multiple forms/hidden fields hack as already suggested, or you can do a javascript onClick for each submit button that changes a hidden field. The problem with the former is if there are other, shared form elements you have to do further hacks (probably javascript) to distribute the information to each form. The latter hack is better, but relies on javascript, which I like to avoid.
What I like to do is
name the submit buttons differently, and use the names as values. For example, if you have
<input type='submit' name='add1' value='Add'>
<input type='submit' name='add2' value='Add'>
and the user clicks on the first "Add" button, you'll get a add1/Add key value pair - you use the name/key as the submit button value and you're set (just make sure your naming scheme won't clobber any of your other form element names).