I have wanted to post something like this at least since I saw a staff member drop all the way to one reputation on the basis of one poorly-received announcment, but thought that it is about time to do so with the recent posting of the above question.
Reputation on a Stack Exchange site is supposed to represent how helpful a person has been to the community. This matters for ordinary users and even elected moderators (who "answer" for their behavior both to the community and to the company).
This idea breaks down when it comes to staff posts on Meta Stack Exchange - a staff member's primary goal is not to be helpful to or provide value to the community, but to dutifully enact the orders given to them by the company. For that reason, let us allow (but not requre) staff to "opt-out" of reputation tracking at least here on Meta Stack Exchange. Their reputation could be locked at an appropriate amount, tracked silently "behind the scenes", or simply not stored at all, but regardless, it would not be displayed. It would probably be replaced with some sort of "Staff" designation, and could include recognition of achievements related to their role, such as employee awards they have received or their latest employee performance evaluation statistics.
I would wish to say that we could expect staff to find the best of both worlds - to make all announcements they need to do as staff but only in ways acceptable to the community, but I know that is not really realistic. The alternative is to push the idea of a reputation "hit" out of the minds of staff so that they can concentrate on their work, and also to discourage members of the community from judging the staff member based on their rep.
A staff flair might look something like this: