There's only so much control you can have over the iFrame. That's a limitation imposed by Facebook because they don't want you (as the admin) to be able to force your users to invite friends and such.
To change the width, I'd recommend setting the columns of users to show (in the JFBCInvite parameters) to 3, which would be a width of 466px. For some reason, FB doesn't give the option of 4 for columns, so that's missing, in case your wondering. That setting is smaller than you're looking for, but should work with the automatic resizing we do.
Hopefully this helps. If you need to modify the template file itself, you can find it in /modules/mod_jfbcinvite/tmpl/default.php. If you have specific questions about how to do something in that file, don't hesitate to ask!