There are a few places (Cairo, Godthab, Chile) that can't be represented by POSIX-conforming strings; for these we'd punt to the "write 400 years worth of data and work modulo 400" approach (leaving off the trailing TZ string).
I'm not sure what the problem is with those timezones. Can you explain?
The problem isn't with the time zones; the problem is with POSIX limitations on describing time zones. The easy case to explain is Chile, where transitions occur in March and October on the first Sunday on or after the 9th of the month. This will sometimes be the second Sunday of the month; other times it will be the third Sunday of the month. POSIX, however, only allows for first Sunday or second Sunday or third Sunday or fourth Sunday or last Sunday. Avoid the temptation to try to "fix" POSIX; the inherent POSIX assumption is that all time zones can be described with two annual transitions that are historically invariant and that simply won't fly in the real world. --ado