Always use Time.zone.now and similar

This is copied from imminence (and many of our other Rails apps), originally
copied from Whitehall.
Avoid time zone problems in DateTime

This is mostly hoop-jumping to make the check_for_bad_time_handling happy.

Date.current pays attention to the local time zone.

I think the old code would have generated a misleading count of days between
midnight and 1 AM.

This is also a touch simpler, which is nice.
Fix test broken by setting Rails' timezone