Hi, I wonder if sound might play a part? I mention it because my Amazon showed no interest in bathing or being misted and would stand miserably in the bath or walk away from the mist. I noticed that when I was drying my hair she would try and bathe in her water bowl so I misted her with my hairdryer on in the background and she went berserk for it! Wings spread, preening while soaked, twisting her head around to get the water everywhere, she loved it. From then on we mist her with the hairdryer on for the noise!
I wonder if the sound of a hairdryer or shower (that we don't have) or a similar loud, nondescript noise mimics the sound of heavy rain and triggers some sort of bathing response?
Might be worth experimenting with this while you're trying new things?