The difficulty of birthdays between Christmas and New Year in Japan

My daughter is born right between Christmas and New Year's, which has become increasingly frustrating to her over the years. I think she has become more and more aware that it's harder to schedule things like birthday parties during this period—we typically celebrate early or late to try and avoid people not being able to attend due to other commitments, for instance.

One year, we tried to order a cake from Ginza Cozy Corner and they said they only had Christmas cakes available at that time of year. Other times we've purchased a birthday cake only for them to add a Christmas message to the chocolate plaque. 

This sums it up ;) 

She often laments that other children born at "regular" times of the year seem to get more of the focus on them for their special day, and I think her feelings are justified. I really believe that every human (not just children!) wants to be seen, heard, and celebrated, and so we do our best to still make her feel important, valued, and loved even though her birthday often gets caught up in Christmas/New Year hype. 

Do you have any Christmas/New Year's period birthdays in your family? How do you celebrate?