Delete link on single-custom.php with redirection

Rather than “still on” page the user actually goes to the link and then sent back after post is deleted. From your description and quick look at code this is probably line that sends user back:

wp_redirect( add_query_arg('deleted', 1, $sendback) );

Since destination is filtered inside wp_redirect()

$location = apply_filters( 'wp_redirect', $location, $status );

and you have that ready-made deleted marker it should be easy to redirect user elsewhere, probably with engineering some checks so that it doesn’t interfere with normal admin operation.