Use a monotonic clock

Generally assume that clock values always increase to simplify reasoning
everywhere clock values are used.  Then enforce that assumption.

Clock values don't really, truly always go up because page reloads &
multiple devices, but since I'm not currently planning to spend the
effort that would be required to perfectly handle this in all cases,
making it happen in fewer cases is a win (rather than just making bugs
I want to fix harder to reproduce).