I agree that a hackabit is not ideal from a refinement standpoint. So why don’t you try a snaffle with hackamore combination? That seems like the simplest thing to do. This one you can use in combination with a snaffle due to the shape of the shanks: https://hermsprengerusa.com/products/kombi-style-hackamore?srsltid=AfmBOoqO_c04CxKkKDPbD6jZN9VWjwo2Slcce9EtCTG5ewT5kDRgxmr9
Second suggestion would be a polo gag on two reins, but it’s a very different action. If she responds well to nose pressure why not just keep it that way?