she wakes should be accepted. My Merriam-Webster gives awake as one of the means of wake, often with up. I use them interchangably as intransitive verbs. I wake up = I awake.
should one be able to hear the distinctions that make ''elles se reveiillent'' wrong?
Elle se réveille = She wakes up = her eyes open
Elle se lève = She gets up = she gets out of bed