Hi all, I wanted to relate something I speculated once I learned about this Time Bastard thing. It is solely based on the fact that time travel "takes as long as it takes" (i.e. the amount of time it takes to complete events is the amount of time that has passed when the time traveler returns) and (of course) one wild speculation that has no proven basis in the game. If this post is a repeat of someone else's conjecture, I wouldn't know because I haven't checked on all other related posts, therefore feel free to add a link to any previous, similarly related posts.
Based on the fact that the time gates "conserve" the properties of time (i.e. the amount of time that would naturally pass) for the individual traveler, this is a suggestion that the time gates should be considered "smart". Regardless of the effect the time gate has for the traveler intending to right wrongs (future or past), time still flows naturally on both sides (at the same 'times' XD ) of the gate. Secondly, even though a traveler cannot escape the effects of time, ANOTHER time traveler can not escape, or, apparently, 'hitchhike' on the effects of a previous traveler. This would suggest that individuals are somehow recognized or generate their own individuality (I would provide an algebraic type example, but I believe it is clear).
So, further, individual time travelers being 'recognized' by these 'smart' gates strongly suggests a link to the whole conservation of energy in the universe. Although the gates are taking advantage of some kind of glitch and allowing time travel, time/space is still flowing naturally in the form of, or at least somehow around or within or both, the time traveler. Until the time traveler returns, he/she/its pocket of conserved universal energy goes with them and is mostly inert until it is returned to its time (in this case, dimensional travel notwithstanding) of origin.
I realize this leaves the question of "Well how is this possible when time branches are created due to actions of time travel in subsequent pasts?" In other words, what is PREVENTING the 'duplicate' of the initial time traveler in a new time branch. Again, I would turn to the 'smart' aspect of the gates. If the gates can 'participate' in time anomalies and utilize time anomalies to generate time travel (in BOTH directions no less) then it could be posited that (without logic or explanation) that anomaly is an energy paradox loop STILL governed by the basic laws of time flow, but not susceptible (or privy) to presence in timeline changes it is directly 'responsible' for. There is no proof that the actions of the time traveler would travel THROUGH the time gate (being subject to all its 'smart' properties and such) as the traveler does, but rather the effects flow AROUND or WITHOUT the gate and are still absolute as the time traveler returns with their 'pocket of conserved universal energy' as I'm calling it. The time traveler's RETURN is quite literally the Chrono Trigger, but only for themselves as dictated by the trope known as Ripple Effect Proof Memory. The Chrono Trigger, in this case, won't experience any of this 'outer' time rippling (or knowledge of it supposedly), but will be crucial to its completion in regards to bringing that rippling to fruition . . . again, for only the Chrono Trigger individually.
Lastly, there is the question, of 'where' this timeline would exist to accommodate the hapless victim of Time Bastard, which is really only touched on in Cross. The biggest enemy here is the whole Schroedinger's Cat scenario, as it leaves everything up in the air until the so-called Chrono Trigger ACTUALLY performs their time altering deeds AND returns or travels or whatever to the thusly affected time periods ONLY via the initial time travel method. As for the 'outer' ripples containing duplicates of the initial time traveler somewhere, there is the explanation of the Darkness Beyond Time. Rather than a poor victim of a future self's time travel being time-nihilated, I think the 'potential' 'outer' timeline effects with a duplicate will flow according to the properties which established the Darkness Beyond Time. This is considering, the 'original' time travelers from the original Zeal incident to be the 'culprits' and subsequent guardians of the everything the Darkness Beyond Time requires to maintain existence, explaining why they are stuck, or in Schala's case, bound and lost.
And just as a fun personal opinion note to add, Chrono Cross is relatively unclear on observable properties regarding dimensions. The Angelus Errare exists as a catered response to Serge's needs after a particular set of events (am I breaking the 4th Wall?). Serge could have gone on his whole life as an anomaly, and perhaps the vortex would never have materialized, even though Serge's existence could, at ANY point, have utilized the oppurtunities potentially provided by it. I like to think it is an ironic term because, truthfully, it is a Godsend for Serge, and secondarily only exists only because of his original anomalous rescue by Schala.