I'm not really sure if your advances will counts for the next years, for example: This week I advanced in some cake extractor and was only 2 left, but i had to go, so i logout my char and enter the next day and I just continue doing the last 2 cities left, but when i came to get my reward with He says to me:
Brutus The Baker: I am sorry, but you did not earn your reward yet.
So I had to make all travels once again.
But, with my mainchar I visited the cake extractors before Brutus appeared and the next ss when he appears in my server i just took my reward without problems.
But anyways once the dissapear you will not able to complete the Cake Extrators part cuz to do it you have to go back to the cake isle everytime, and if the cake isle dissaper you can't complate it for next year.