Schala is transported to "The darkness of time", where unused timelines end up, somehow, she meets up with lavos, or whats left of it, they bound because Schala was the arbiter of the flame in Zeal (this fact is not completely reliable, but anyway...), and lavos, or the "Devourer of time" starts to gain power to destroy time and etc etc etc. The Chrono party's destiny is unknown, except by a few facts like luccas death or incident by the hand of lynx, robos joining the Mother brain's circuits, the fall of guardia by the hand of porre, and some other. Serge is a new guy, that is the new arbiter of time, which means he can bound with de devourer to destroy everything. The game its about this guy, Kid, who is Schala's clon, and the master plan made by Belthazar, but i guess there´s no better way to explain it than playing the game. The game follows the "all side quests completed" ending, and it is not, in any way, a story telling what you proposed.
I am indeed sorry if this info is wrong, im kinda stupid after all, any help would be awesomely received.