How to port vertical tabs functionality for custom node module to Drupal 7?
While driving me nuts yesterday, I started over again today and cleaned up the module a bit.
During that I tried to add another vertical tab again (#4) and this time it worked. By accident, I did re-use a group name and by this I finally was getting fully aware of how this is intended to work.

My mistake was to create a form element of type "vertical_tabs" for each first-level fieldset. But it is sufficient to only have on "vertical_tabs" form element and assign all fieldsets to that group (they actually are grouped then).

So, everything is fine with my code above but the last three lines are only required once.