If you look at the end of the function get_cancel_comment_reply_link( $text = '' ) in the file wp-includes/comment-template.php, you see the filter cancel_comment_reply_link.
return apply_filters( 'cancel_comment_reply_link', $formatted_link, $link, $text );
It may work.
In an environment without third party code, get_the_ID() should give you the correct value. It sounds like some plugin is interfering with this.
So you can do what they forgot and simply call
in your footer before you need the values.
Ok got it, knew there must be some built-in WP solution to this. Simply call wp_get_referer() in your callback (for details, see this).
At least it's working as I need it, let me know if there's any better solution.
Thanks to @Tom J Nowell, we should also mention that referrers could get stripped for privacy reasons or similar. To thus be on the safe ...