I’m afraid you may be on a long road to recovery. Something similar happened to me at the end of June. I’ll go through it to give you an idea of the timescale and the complications I’ve faced that might have made things worse for me.
In my case I was switching to https, except it wasn’t a straightforward move because I couldn’t afford a wildcard SSL certificate, so I had to move all of my pages off subdomains onto my www site.
It absolutely trashed my traffic, I was at about 4K at the time, about half of which was from Google. (This is after suffering from an algorithm change in March that dropped me from about 10K). I dropped to about 800 visitors.
All of my rankings fell. Some pages disappeared completely for a couple of weeks.
I believe most of the traffic I lost was from very long tail and unique queries that use the “neural matching” algorithm, although that’s speculation.
I’ve spoken to a couple of SEOs online who think I might have been put in a spam sandbox because I have a lot of exact match backlinks, just as a result of the way people share my site. I am 100% white hat.
I’ve also considered the possibility of a mobile first ad related penalty, as Google “helpfully” switched me to mobile first about four days after I initiated the site move, and a handful of my pages violated the 30% height rule (which I didn’t know about) but I just don’t know.
I made a lot of site quality improvements. I’ve honestly been working twelve hours a day ever since it happened.
I had a partial recovery during the mini core update on September 27th, and I almost have the same traffic as before the move to SSL.
I’m not sure exactly how it works but Google seems to need to respider and follow backlinks before it really understands that a site has moved.
Google has now respidered all 60k of my backlinks. I still don’t have my rankings back. I was in position 1-2 for almost all of my pages. I’m currently in position 3-4 depending on the page, though I’m starting to see the occassional position 2.
I’m starting to get very long tail “neural matching” type searches back now, though that could be because I’ve made a lot of changes regarding relevancy and ensuring my topic coverage is a lot more comprehensive.
I believe I will have to wait for the next core update before I see a significant improvement. I’m just hoping it comes before Christmas so I can afford to live again!
I’ve read stories from people who’ve had bad site moves who said they just reverted back to their old domain and recovered their rankings and traffic.
If I were to do a site move again I think I’d try and get a second site ranking with new content and then move things over a page at a time, as not to trigger any sudden shocks to Google’s algorithms and over-zealous spam sandboxes.
(I wanted to move my subdomains one at a time, except Google responded to the SSL certificate install on my www subdomain by changing all of my other subdomain addresses to https in the serps which broke the site for users because I didn’t have the wildcard SSL, which forced me to do the site move all at once.)
I think if you have a lot of backlinks coming from one blog that could have triggered a sandboxing effect, if the sandbox is real.
It may just be a case of waiting it out. I’ve heard site moves can take six months to see a full recovery.
Edit: by the way I couldn’t do an address change in webmaster tools because you can’t redirect to specific urls. That may have made things worse for me.
[edited by: broccoli at 6:25 pm (utc) on Nov 12, 2018]