Hi Dimitrios,
Sorry for the confusion. There is in fact a safe way to go about this. Since your site is currently showing two different pages on the same URL (big no-no according to Matt https://www.youtube.com/watch?v=GyWx31GeQWY), you can do any of the three with the following consequences:
Keep the default domain as the English language as it's been indexed by search engines as of now, and then add a /de/ subfolder for your German visitors. You won't lose any rank in the short term since you're not changing anything that search engines already see, your just adding pages. But as your 70% German users trend toward the /de/, these pages should out rank the default domain in time.
On language switch, your visitors are redirected to the homepage from any other page, so your site wouldn't take that big of a hit by keeping the default domain home page and adding two subfolders /en/ and /de/. In this case, the homepage could be either language, but since the English page has been indexed already, this would be the safest way to go for the default domain. If you're goal is to rank the German site higher under the current conditions, don't worry about the hit. Do what's best for your visitors and make German the default language.
And lastly you could cater to your German visitors by making the default domain German and adding an /en/ subfolder for English. Again, here your site has already been indexed in English and only English, so I imagine you'd take a hit in the short term as the search engines reindex, then you'd recover in time assuming your keywords are in German.
One more option I just realized you were considering was redirecting visitors to either a /en/ or /de/ without a default domain home page. Since this is the page showing on SERP results, it would be a bad idea to remove that page.
Just so you're aware, your English site shows in the German results only because it's the only site Google can see. As far as I can tell, there are no URL parameters to indicate to any search engine which version is English and which is German. Once you fix that, you might actually rank higher.
Hope I got your question right this time. I'll just add here that I run a multilingual e-commerce site in Taiwan with Chinese and English. I set the default domain to show Chinese and added an /en/ subfolder for English. Over 75% of my Chinese keywords rank #1-3 while only 20% of my English keywords rank #1-10.