Sigh. This is the part where I prefer the way Radical Dreamers handled this. Kid = Schala = Kid, it's all clear-cut, and Serge and Kid can marry and Janus can be the brother-in-law from hell, and maybe Lucca's still around and they find her too, and it's all one happy kickass family with all my favorite characters in it...
(For the record, I sort of had a 'they got MARRIED? WHAT?' reaction to this too at first, since Serge and Kid just seem like really awesome friends during the game. But those're my favorite couples, anyway, the best-friend type, and that doesn't mean they can't get married.)
That said, there's got to be something to the "Schala 'Kid' Zeal" signature, and frankly, this is one of those parts where Chrono Cross gets nonsensical and convoluted and annoying and so I just go with what I want, which is Kid gets Schala's memories and everything is happy.