Help, I crossed the date line!

What could possibly be the problem of crossing the date line,  that is going over this imaginary line on the world map somewhere between Australia/Asia and America, where the date changes? Not much, unless your name in Phileas Fogg and you’re trying to go around the world in 80 days ;-)

… Or unless your name is Moshe Levi and you cross the date line during the period of Sefirat Haomer . This is the period between Pesach and Shavuot, where we count each day just as the Jewish people counted the days in anticipation for the giving of the Torah on Mount Sinai (and just as kids count the days until the end of the school year!). So every evening, we recite a blessing and say “ today is day 23… 24 etc…” . So far, so good…

But what happens if Moshe Levi leaves California on day 23 of the Omer and crosses the date line to get to Australia. Over there, it is already day 24. So when he arrives, does he skip a day and continues the count with day 25 as the rest of the local community (which does not make sense, after all this a count, where the days are supposed to add up) or does he continue his own personal count?

Another problem is the holiday of Shavuot: the Torah instructs us to celebrate it on the 50^th day of the Omer… So when should Moshe Levi celebrate and eat cheesecake? Together with the community or one day later according to his own count?

Any ideas?