Understood. Because she is so very persistent I would try using the rake above her head and twist it. Moving shadows above their heads are very intimidating. She needs to think you are the bigger bird. I would also only move in ways that take space (forward), rather than yield space (stepping back).
I spent some time with natural horsemanship trainers and one of the concepts they teach is "Do as much as necessary but as little as needed".
Meaning you let the animal set the tone.
If they're confrontational, you act as aggressively as needed to get them to back off.
When they retreat, you let them, and don't try to punish them or scare them further over a behavior they're not in that moment displaying.
With that approach, you know you are not abusing an animal, you don't have to feel guilty later, and you don't accidentally create more problems later.