deiyzooger: That is true we do not blow shofar at nigh but we still daven and maybe that is good enough.The Rama was only concerned by day and not by night as you can see from his wording and everyone else peirush.
Sam2:I don’t see the problem of sleeping before chatzos from the Rama or the Mishna Brura.They quote the Arizal for the davening and teikos part I don’t see the reference you mentioned unless I missed something.