I am attempting to do the same exact thing.
We ended up using the WP API plugin, and modifying the output of the feed to include custom fields. The problem with this approach is that the feeds aren't cached and we have no way of differentiating between post types. So the out json feed is messy, but it works. We are using the feed for an iOS app.
The Plugin: http://wordpress.org/extend/plugins/wp-api/
We modified the output of the feed like this:
"'Name' => get_post_meta($value->ID, 'CUSTOM-FIELD'),
In this example URL: http://www.domain.com/?wpapi=get_posts&dev=1&type=posts the above code would go around line 270 of "get_posts.php'.