CT and PET coregistration with alternating results

Are you sure that fixed-moving approach is required? CT / PET should be aligned in physical space. You could check Frame of Reference UIDs of the series (if they were not messed by a bad anonymizer).
S. this @zivy post

The essential line is

# Resample PET onto CT grid using default interpolator and identity transformation.
pet_image_resampled = sitk.Resample(pet_image, ct_image)
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