I like the general idea, and I can definitely see the Ellimist and Crayak having had a hand in the events of Gone.
That said, I think some of your character assessments are a bit off. Sam = Jake, Rachel = Brianna, and Ax = Jack I can definitely see. You've got your two reluctant leaders who won't step up to lead until they're needed, you've got your two psychotically brave girls with just a touch of "I'm better than you" arrogance (although, it's still worth noting that Brianna lacks the insecurities that Rachel keeps buried deep down below her mask; Brianna doesn't wear a mask, I think she's just psychotically brave), and you've got your two tech geeks who don't really understand the nuances of human society. You're pretty spot-on with those.
That said, I pretty strongly disagree with the rest. Tobias is not Edilio. Edilio is a smart, practical, with-it kid who knows how to get what he wants even when other people try to hold him back. He can look at a situation and know what to do. If not for Sam and some of the other people with powers, he would very likely have become the leader of the FAYZ. Tobias, as much as I love him, was FAR from being that gifted at dealing with what life handed him. It took a war, and a higher cause beyond himself, for him to even try.
Cassie is not Astrid. True, they share a certain smug superiority because of their respective moral beliefs. But, where Cassie was only manipulative when she had to be and seemed to resist the idea of ever being ruthless, Astrid's default state seemed to be 'manipulative and ruthless.' It wasn't until quite late in the series that she ever even developed qualms about being the person she is; something that would have happened MUCH sooner with Cassie. She was also much smarter than Cassie, at least in terms of intelligence becoming part of her identity (at no point did Cassie ever consider herself a 'genius' the way Astrid was).
Marco is not Quinn. They share a sort of goofball outlook on life in the beginnings of both their stories, but the similarity pretty well ends there. Where one (Marco) rises up as sort of a strategic general, the other (Quinn) really just wants a simple life of fishing. It takes Quinn until nearly the end of the series to finally realize that it is within his power to strategize and use his cleverness to his advantage against an enemy. As such, it's pretty clear that he lacks Marco's innate ruthlessness.
David is not Caine. Caine had a strong charisma about him that made people want to believe and follow him. If David had had that, he wouldn't have had nearly as many problems with the other Animorphs as he did (might have even gotten away with some of the stuff he tried to pull on them). And while they share at least a few of the same ruthless tendencies, I think that David was originally a good person who turned bad, as shown by the fact that he couldn't kill the Animorphs as humans, making up all that bull that it was okay if he killed them as animals.[spoiler]Caine was exactly the opposite; a bad person who turned good. And he clearly had no such compunctions about killing humans.[/spoiler]
That said, I don't see why you're trying to shoehorn them into being the same people, anyway. The Ellimist and Crayak have played loads of games, with loads of different pieces. Who's to say this wasn't just the start of a new game, instead of a continuation of the old?
EDIT: I changed my mind, Ax is not Jack, either. Ax has a strong (if occasionally misguided) moral center and a powerful sense of honor, in stark contrast with certain actions taken by Jack early in the series [spoiler]such as joining sides with Caine just to be able to feel special.[/spoiler] Even later in the series, Jack is still a far cry from being the military-minded cadet that Ax is [spoiler]and even has to be forced to fight against his will.[/spoiler] Where Jack is just a scared kid, Ax is a soldier. Some of this is probably due to upbringing, but some of it has to be innate; I cannot see a person like Jack ever being able to become a person like Ax.
