And just as I was finally calming down enough to go to sleep, I got another email notification. Turns out I got sent the wrong date:

-
I know that you received information from the Recruiting and Placement Dept.
in the Tokyo office asking you to arrive in Japan in the fourth week of
March. Unfortunately, Tokyo had not received updated assignment information
from our office and so the specifc date that you were given was incorrect. I
bear full responsibility for this error and apologise for the confusing
information that you have received.

Due to the later starting dates of the Hitachi City and Iwate Prefectural
Board of Education contracts, you will be receiving special training in
Hitachi and thus should purchase tickets to arrive at NARITA INTERNATIONAL
AIRPORT on APRIL 4 (Sunday), NOT March 22. Please proceed to make
reservations to arrive on April 4.

As you will be catching a bus from the airport to and travelling directly
from the airport to Hitachi, please try to arrive as early as you can on
April 4. The last bus leaves Narita Airport at 8:45PM, so if you have no
choice in flights it shouldn't be a problem.
-

So the new date to count down to is April 4th!