OK. Some new news. If I feed her really small amounts of food (like a tablespoon) she is not throwing that up (at least not yet).
This is food she previously had vomited when I let her eat as much as she wanted.
So food itself doesn't seem to be triggering the vomiting, but rather a certain amount of food.
She's not overly pleased that I'm feeding her such small amounts, but for now that's the plan, so that she can get the nutrients she needs.