EDIT 19/6: the issue is apparently solving itself
Unfortunately I cannot see any indication of what worked. It could be the spammy-looking domain which we disavowed links from, but it can also be a glitch of Google's own algorithm. The DE-AT links appear unchanged in webmaster console (still showing a lot of links) - so we concluded it was probably not that. We are happy and relieved that the rankings are going back up, but we do feel frustrated and insecure about our future on SEO since these drops are affecting our business dramatically and we cannot really control them.
Original post
We have a website that is present in different markets in Europe. Therefore the content is specifically targeted to specific countries using a TLD strategy (we have site-name.de, site-name.it, site-name.es, site-name.at, etc.)