timezone setting in the current year and for 100 years back, rather than
always examining years 1904-2004.  The original coding would have problems
distinguishing zones whose behavior diverged only after 2004; which is a
situation we will surely face sometime, if it's not out there already.

In passing, also prevent selection of the dummy "Factory" timezone, even
if that's exactly what the system is using.  Reporting time as GMT seems
better than that.