Honestly looking at this, I can see why May did so well in the second phase.
First phase was fear which can't be ignored because it's magical fear, the acceptance technique would never work because it's magically induced as she said, and the fatigue was a bi-product of that fear.
The second phase being pain however, even if magically induced, can be ignored with the acceptance technique, and more on point, because May realised instantly that the harm wasn't permanent she could use it to experiment, feel degrees of pain whilst knowing that no real harm will come to her. It's not about facing your mortalitiy because you know you aren't going to die, after that it's acknowledging what pain feels like and accepting that pain.
I actually wonder if this is some kind of warrior training. Phase one forces you to face a fear that cannot be faced, whilst pushing you to a physical limit. The second phase builds on that fear with physical pain, but no actual harm comes to you so it's learning to fight on in spite of the pain, or in maytags case become accustomed to it.
It's not something somebody who's emotionally dead can deal with, but somebody who has near perfect control of their emotions could.
I wonder if stage 3 will be something akin to a full psychological assault. Phase 1 is artificial fear, phase 2 is artificial pain. What if phase 3 is more real than that, showing you what you truely fear the most, causing pain in ways that affect you not only physically but psychologically.
While May can ignore the pain happening to herself, what if phase three were to be something along the lines of visions of Bernadette being raped and tortured, even if she knows it isn't real, I don't think May would be able to ignore it.