Manager vs. Verwalter
Administrator is used in the context already for another role, so not available.
I don't agree about the connotaion: Manager is used in the press not with a bad connotation as far as it is: daily press (spiegel, FAZ, Zeit, Handelsblatt, business categories, business magazines, Wirtschaftswoche). Typical usage in articles is "Topmanager", "Spitzenmanager". SPON runs even a column to emphasize good performances of the middle management ("Nach Dikatat verreist"). One of the major business magazines is named Manager (http://www.manager.de/).
Exceptions are commentary ("Kolumnen"), especially of left wing bloggers (SPON without Fleischhauer). The other exception is reporting on law suits on managers.
On Wikipedia they use "bureaucrats" for a special role ;-) there i would agree on a negative connotation when i never heard the word with a good connotation :-D Did you?
What about a more positive Word which stresses the leading function either: "Leiter"? Or, cause of managers relation to projects on iNaturalist, it could be more precise: "Projektleiter"?
I think most would like a role with that name, probably more than "Verwalter" and even "Manager".