This dilemma cannot be unique to you. I would suggest a quick call to your medical team, who must have experienced it before, and see what they advise. Presumably if they needed you entirely unfed they would have said so.
I suspect that you may be taking "zero fat" rather more literally than it was meant, so that undressed green veg and most raw fruits would be acceptable, but your medics are the ones who can keep you straight.
If they cannot advise I would (personally) be considering whether I am with an appropriate medical team, late in the day though it may be.