Facebook – Can’t sign up a new Facebook account for the business

As I said in the comments

I have read in some places that the username is held for a bit (a few weeks) before it's released. Now it's not to say it's not possible; Zuck had his personal profile merged with his page and got a permanent redirect on one, but it's whether Facebook is inclined to help every soul out there.

So it is possible some lag time is held to account for name squatters and vandalism. Seeing that you were able to make the switch makes this even more valid. I would imagine it is not something Facebook is trying to make widely known as this would just increase the number of complaints from users that their username switch isn't working.

From a technological perspective, the important problem which you are addressing -- that of a disgruntled admin "hijacking" a Facebook application -- does not seem to currently have a solution.

This problem is virtually identical to that of a Facebook page being similarly hijacked, and as mentioned in this article on Mashable from Sept. 2011, the latter seems to be a flaw in Facebook's security architecture. Judging from the articles found in a Google search today for "hijack facebook page disgruntled employee", it would seem that this flaw has not yet been fixed.

Moreover, technologically, this danger exists regardless of the legal nature of the business entity involved. So, I don't think that the perspective of an LLC changes anything.

From your description of the "repeating cycle," I suspect that you were not asking for a legal perspective on how to prevent or manage this problem, say, via clauses in contracts ... etc.