At the moment, there’s no easy or great way to set some default widgets and widget values. This is the case with WordPress in general, and not just BadgeOS’ plugin.
That said, I think some filters applied to the default values for the widgets is not a bad idea. I’ve talked with our other developers and they’re fine with the idea. So hopefully in a future release we’ll be able to let users set default values that way.
If you’re not familiar with hooks and filters, you can read up on them at http://codex.wordpress.org/Plugin_API
Thanks Michael, I found something that works for my situation. I am able to display the users earned badges from the main site on new sites and change the default widget title using the following code in the appropriate template file:
<?php switch_to_blog(1);
get_sidebar();
the_widget( 'earned_user_achievements_widget', 'title=My Latest Badges', 'before_title=<h3 class="style-sidebar">&after_title=</h3>' );
restore_current_blog();
?>