I would prefer loose, to be honest. Rather than trying to determine the fates of specific characters, a new story ought to focus on expanding elements of the Chrono world. For example, the game could detail the struggle of the Iokans and the Larubans against the Reptites right up until the fateful day Chrono and friends show up(or perhaps even show the version before they interfered in time!)
Or it could show the rise of the Kingdom of Zeal, from whatever humble beginnings it came from to the centuries of existing of the floating isles.
Maybe perhaps it could chronicle the formation of the El Nido island chain by Fate, or the various events in both Dinopolis and Chronopolis prior to the Time Crash.
The sky is the limit, basically. Expand your imagination. Enrich the world.