So when protractor times out, the error message shows a link to the faq. Right on top there's the explanation for this problem. Apparently the app sends continuous requests (maybe because I am using socket.io), so Angular is never finished.
This problem has nothing to do with the separate apps.
The issue link was very helpful. Since I am not willing to touch any of the pages code I settled with
browser.ignoreSynchronization = true;
and
browser.sleep( ... );
The tests now work as expected.