What are your preferred ventilatory settings/mode(s) for patients with acute hypoxic respiratory failure presenting with severe biventricular dysfunction in cardiogenic shock?

This is a great question - and, unfortunately, one that doesn't have a robust evidence base upon which to formulate a particularly informed response (at least nothing that has looked a hard outcomes like mortality or duration of mechanical ventilation). I go back, however, to the basics and a mantra that I use frequently when it comes to mechanical ventilation in critically ill patients: "Rest when you want them to rest, work when you want them to work, and don't mix the two." What I mean is that if you have chosen to invasively ventilate a critically ill patient with cardiogenic shock, you should at least attempt to minimize the work of breathing - choose a controlled mode of ventilation, optimize patient-vent synchrony, apply appropriate ...