Translation:You should sleep.
So, in reference to the sentence 'je zou je moeten schamen!', if I wanted to say 'you should be asleep', it would be 'je zou je moeten slapen'?
No, "schamen" can be reflexive, "slapen" cannot.
You can say "You should be ashamed of yourself" - "Je zou je moeten schamen", but that does not work with "sleep" or "slapen" in Dutch.