Unfortunately trains will be busy, especially on Sunday, January 3. Monday, January 4 will be the first day of the work so everybody will be heading home on Sunday, January 3. Yes, heading to Kanazawa on January 3 can be less crowded than heading to Tokyo. But still you will need to be flexible, the specific train you want can be booked and trains with seats available may not be on the time of the day you want. Also your situation on December 27 and December 29 you are planning on specific trains. If Sunrise Seto are all booked then there really is no alternative, or Plan B as far as train schedule is concerned because Sunrise Seto is the only overnight train. As for Ufuin - Hiroshima on December 27, Plan B will be to take regular trains, not tourist train like Ufuin no Mori.

JR tickets go on sales one month in advance. During major holidays, such as New Year, it is not unusual for some trains to sell out on the day of the sale a month in advance.

It is correct that JR tickets are available in Japan only. You may try Japanese travel agencies which has office in the U.S., such as JTB. But I know JTB does not do this in their U.S. office for purpose of getting JR ticket alone. If you have purchased international airline ticket to Japan through JTB, or purchased a tour package through JTB then they may do that by asking office in Japan to get JR ticket and you may pick up JR ticket at JTB office in Japan once you get to Japan.

But same time during busy travel season, even JTB will not guarantee they will able to get specific JR ticket of your choice.