I've never used a gyro controller before and I'm probably thinking about it a little bit differently than normal, but let me know if this is possible in general and for Doom: The Dark Ages specifically:
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Flip the controller towards me to raise my shield - basically map "point the controller to the ceiling" to a keybind.
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Push the controller forward quickly to throw my shield - map direction and speed to a keybind.
Does this sort of thing exist in gyro controllers and games?