Finally got a chance to poke around and the white screen fix is VERY easy.
In bc-oauth-loader.php (btw, proper naming convention for this file should be bc-oauth.php), you simply need to add the following hook:
add_action('init', 'bc_oauth_init');
The problem is that the login action is trying to use wp-load.php, but there is no hooked function there to catch the login request. The init function, bc_oauth_init(), is hooked to wp_ajax, which only used by requests sent to /wp-admin/wp-ajax.php - since I don't know if that's actually used or not, I simply added an extra hook that allows bc_oauth_init() to catch requests from wp-load.php.
Everything works great, now.
;-)