How can I get daydream mode to remain active throughout the night when using the wireless charger?
Since wireless charging actually stops charging at 100%, daydream will not stay active.  There's a open issue for this at https://code.google.com/p/android/issues/detail?id=48980

As a workaround, you can root your phone and, go to a command prompt and type the following:

su
svc power stayon true