Amanda Unvarnished

As far as I can tell, melody isn't dependent on time of day, but on the other hand there's nothing governing it, so if you wanted to you could have a melody for morning weekday, and then one for nighttime weekday, same for Shabbat, ETC. It's one of those songs whose lyrics will fit a ton of melodies. Do you have a favorite siddur?

It's been included after the bedtime Shema for a long tome. The old Birnbaum Siddur has it there, as does ArtScroll, of course. So I'd say at least that there's nothing that says it can't be there.