We've missed your updates @UnwelcomeStorm, It's good to have you back. I have to admit, one thing I found curious in my re-read of your story was the placing of the tokens in the ceremonial box marked with the Chinese Zodiac. Is there something big tied into that point, since alot of the times they show up it is at the end of the chapter acting as a cliffhanger. Also, wow, that was a fast ending of the E88 from the last time I saw them. I thought they were going the path of the Local 88, or am I getting you and Selector's version of the story mixed up?
Since you are asking about this I'm going to guess that you have not played the video game this is a crossover with. In the video game, you could collect beads. The point of them, was that they basically unlocked cheat codes or extras such as the ability to change what breed of dog amy was or invulnerability if you had all of them. Thus in the context of this story it is most likely simply making Sunny stronger.