I don't think the current ICU API allows this bug to be completely fixed.
Right now, the code cannot control the time zone used in date/time formats
that appear inside complex subformats. See the comment inside
umsg_set_timezone().
MessageFormatter::parse and MessageFormat::format (and their static
equivalents) now don't throw away better than second precision in the
arguments.
It's already bad enough that in MessageFormatter and IntlDateFormatter we
use seconds since epoch instead of milliseconds since epoch, deviating
from the ICU date representations. But we don't need to throw away extra
precision when parsing dates; we can keep the seconds since epoch
convention and return non integer doubles with only a small BC impact.
Note that we already could return doubles from MessageFormatter::parse if
the date was sufficiently in the past or in the future.