I suppose there are as many cultural assessment tools as there are organizational consultants. In fact, I have one of my own based on living systems. I had assumed that Hofstede's factors were aimed more at assessing nationality differences, but you seem to make good use of them in a single setting. Why not?
You did not mention whether the organization was in a crisis or not. I assume not in which case it is a good idea to take it easy with change until the new leader knows the lay of the land. I don't know if you took a look at risk assessment because that would certainly be a factor in a healthcare setting and behaviors that put patients at risk would have to be handled immediately, no matter how much it offended staff sensibilities.
When there has been rapid turnover of management that is a suspicious indicator to me that something is rotten at the core of the origanization, perhaps more than just a mismatch between management and staff styles. Especially if the enterprise is not in a crisis mode financially or otherwise, i.e., it is meeting its basic obligations to customers and stakeholders but just has this "people" problem. The leader who can turn around a crisis is not always the leader you want for the long haul, as difficult decisions will generate a residue of resentment toward the crisis manager. It has happened to me in my career and the mistake I made both times was in not firing the dissidents up front, but instead trying to be inclusive and conciliatory with them.
It's like Ricky Nelson sang in his 1972 classic, "Garden Party": But it's all right now, I learned my lesson well.
You see, ya can't please everyone, so ya got to please yourself.
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