I sent an email to Alfred Geroldinger with a link to this thread. Here is a summary of his reply (I'm posting with his permission):

 - The structure of minimal zero-sum sequences of maximal length over $C_3^n$ is unknown.
 - Lemma 4.2 in [Geroldinger and Schmid, J. Korean Math. Soc. 56 (2019), No. 4, 869-915. DOI: [10.4134/JKMS.j180467][1]]gives the structure of minimal zero-sum  sequences of maximal length over Abelian groups of rank two.


  [1]: https://jkms.kms.or.kr/journal/view.html?doi=10.4134/JKMS.j180467