One of my favorite brainstorming strategies is imagining how another person might solve the problem or approach the task.
I'll give you a personal example. I'm thinking of writing a film or play about how political polarization affects a family, with a Christmas family get-together as the setting and occasion. How to give it a fresh angle? How would the three people above approach it?
BILLY WILDER is noted for his witty approach to comedies like "Some Like It Hot," and "Seven Year Itch." I imagine a Wilder-style approach would be a smart comedy, maybe told through the eyes of a recent addition to the family (the new spouse/partner of one of the family) who, to be accepted by everybody has pretended to agree with both sides--and of course runs into big problems when the whole family gets together.
MICHAEL MOORE is noted for documentaries like "Bowling for Columbine" and "Fahrenheit 9/11." He might take a mockumentary approach to the event, perhaps with a psychologist stopping the action to explain what's going on and, if it's a comedy, getting it totally wrong; or maybe the shrink has been hired by the patriarch of the family to intervene and bring peace to the family but of course screws it up and only makes it worse.
STANLEY KUBRICK is known for "2001," "Eyes Wide Shut," and "The Shining," among others. Although there are moments of black comedy in his films, I think he'd be more likely to treat it as a dark psychodrama, perhaps leading to the total breakdown of one of the family members, with deadly consequences.
Of course, your "X" doesn't have to be a film-maker. It could be anybody whose way of thinking you're familiar with and admire. The next time you're stuck or just want a bit of extra inspiration, try the "What would X do?" method.