Disable permalinks, but allow RSS feeds

Have a custom post type event that needs an RSS feed (/feed/?post_type=event) but should not generate permalinks (/events/title-of-post).

Problem is that the publicly_queryable argument for register_post_type enables both RSS and permalinks.

'public' = false, //private, turns off permalinks and more
'show_ui' = true, //allow edit via wp-admin
'publicly_queryable' = true, //turn on RSS for events, but (whooops!) also turns permalinks back on

Is there a simple way to enable the default Wordpress RSS feed for a custom post type without generating permalinks? (Or will I have to make a custom RSS feed using add_feed?)