Reason for the gender change
I saw a "Shakespeare Revisited" show, presented by Trevor Nunn (who did an excellent 'Twelfth Night') that made the point that with a male Prospero (as per the original), you're involved with possible Oedipus conflict and competition for Miranda's affections between Prospero and Ferdinand. With a female Prospero, that's all put to one side.
My paraphrasing. And separately, wasn't Helen Mirren wonderful in this role?
------
To different minds, the same world is a hell, and a heaven. J B Priestley