Am I alone in thinking this is not some casual detail in this narrative?
"Long story short, she recently suffered what could be described as a psychotic event and is homebound, bedridden and horribly depressed."
That "long story" is way too short for any one here to offer relevant thoughts, let alone suggestions or recommendations, about diet of all things.
"We're friendly but not the best of friends so it's going to be hard for me really lobby hard for her to try animal fat."
Especially if she were a friend, there are good reason why for you to "lobby hard" should be difficult.
The person who most needs your attention is — you. As you note, it's a stressful time. Step back from the drama. Crazy or not, she's She's not being force-fed the bananas. She's making intentional choices, based on her sense of priorities. With all due respect, you should be doing the same. Love your friend. That is, accept her exactly as she is, and exactly as she is not.