Chiming in to say my BP is just as picky as yours, OP.
She has to be out and actively hunting to strike. Prefers the f/t rat extra warm. I have to be almost completely motionless.
If it's too late in the evening and she's on her way back into her hide, I can either throw the rat away now, or leave it the cage and throw it away in the morning.
If she strikes and misses, game over.
If she strikes and coils but drags herself/the rat into the water, game over.
I can't prove it, but I also think she's tentative about rats that are size outliers in the multi packs.
She's a healthy size and shape, so it's more funny than frustrating. If she was consistently not eating and losing weight I'd probably try to find a perfect ritual that works.