Don't tie off to saddle. Bad idea.
And Tinyliny has it right, she is giving you cues, that she is getting ready to do it, you are just missing them.
If you will watch her ears? More than likely she is telegraphing intent, by twitching one back and one forwards, meaning she is "thinking" about what she wants to do. Get after her hard and heavy and make her move.
When you let her get that head dropped then you are pulling against the full strength of her neck muscles, and you are not going to win.
You have to stop her before she even starts good, by being decisive about it.
Don't correct her in a "oh, poor hungry horse, I can't control what you do mood," but more from a "oh no you don't mood" like you have towards an annoying little brother or cousin.
Be firm with her. And don't baby her, or chit chat to her about it either. Just correct, and move on.
When you overpraise, especially for doing something that is a no-brainer, it builds it up into a much bigger deal, and can lead to more problems.
And when you do use voice, make it firm, not whiny.