I would start out by making sure you put back the analytics tracking code, since that's not there right now (checked both with Google Tag Assistant & in the source code). So it makes sense you can't see any traffic from search, since there is no tracking. That probably explains a lot of it.

Google do not use it in a page's ranking (see here: https://www.youtube.com/watch?v=CgBw9tbAQhU). And since the referral spam is never actually on your site, but only activating your tracking code it shouldn't hurt you.

Besides, I don't think I've seen a site out there who hasn't been hit by referral spam. Some haven't been hit as hard, but still have seen it to some degree. Just set up some filters & segments so you can analyse on the real data. I found it very helpful to read this and this.

I can only agree with what Logan said here.

I would say, that not all directories are a waste though. If you happen to find a directory with good authority, is still being maintained and is relevant to your niche or location, then I would say go for it. Just always think whether it's worth it or not to go for it. If you're in doubt, then that's probably a sign you shouldn't waste time on it.