Possibly you could use the same logic as The Events Calendar itself? For instance, if your slider essentially is built around a loop you could use that or similar logic to skip iterations.
Is there a way to somehow have a “event-passed” category (ECP does add the event-passed DIV with this information to the post in single display) added to all these events
That’s an interesting idea – the short answer is this is definitely possible. You’d need to decide whether this would be handled automatically, behind the scenes, and if so would a scan of categories be made on every request or would you run this as a scheduled task? Alternatively would you set up a sort of batch-script to handle this and run it whenever you felt there was a requirement to do so?
There are a few challenges there and you’d need to figure out the best strategy to meet your/your client’s requirements.