Hast Du es mit dem Personalausweis versucht?
Auch laut Timatic reicht er:
Passport required.
- Passports and/or passport replacing documents issued to
  nationals of Germany must be valid on arrival. 
Passport Exemptions:
- Holders of a National ID Card issued to nationals of
  Germany. 
- Holders of a German:
  Travel Permit Issued in Lieu of Passport ("Reiseausweis als
  Passersatz"), accompanied by an expired German passport or
  expired German National ID Card; or
  Travel Permit Issued in Lieu of Passport for Entry into the
  Fed. Rep. of Germany ("Reiseausweis als Passersatz zur
  Einreise in die Bundesrepublik Deutschland").
- Holders of a German identity document ( Kinderausweis )
  issued to children up to/incl. 15 years of age. 
Visa required, except for A max. stay of 30 days for holders
of a National ID Card, issued to nationals of Germany. 
Visa required, except for A max. stay of 90 days: 
 - for nationals of Germany not holding a National ID Card;