I do recall your Assassin of Time idea and how intriguing it sounded. What sort of connection would this character have? Would they simply be a host body? would they have free will? partial will/Lavos influence? Would they have exponential powers/time travelling abilities? Do tell.
So my concept existed in a post-Chrono Cross timeline in which, after the events of Chrono Cross, Schala emerged from the Time Devourer and realized that Project Kid and all the events surrounding it (the creation of Chronopolis, the Time Crash, the timeline changes in which El Nido is created by the stranded descendants of Chronopolis) essentially doomed space-time by the creation of an Assassin of Time.
I didn't fully vet the concept, but the Assassin of Time (also called the Enmity of Lavos) was essentially a living embodiment of Lavos in human form, the goal of which was that Lavos created a human avatar, stripped it of all knowledge of it's existence, and sent it to earth to live a life as a normal human. The goal was that the human would eventually "mature" into the Assassin of Time and be reabsorbed into Lavos at an earlier point in history (pre-1999AD).
This was done so that Lavos itself could absorb the one thing that allowed it to be destroyed in the Chrono Trigger timeline: the sheer willpower of humankind. Lavos, who is so alien it barely understands the small scope of humanity, realized that it needed to understand humanity in order to defeat it; it needed to understand love, hope, willpower, and the drive of self-preservation. These were foreign thoughts to it's alien, non-linear timeline existence (I mean, it's core did live in a pocket dimension of sorts). By creating the Assassin of Time and reabsorbing it, Lavos would gain those traits and essentially alter history and be able to stop Crono and company, altering time so that they are unable to defeat him.
So back to Schala... and Chrono Cross. Serge was actually an unrealized Assassin of Time (which is why he was called as such by Lynx on the Viper Manor balcony). Even after the events of Chrono Cross, his existence - and the powers he gained in the Chrono Cross element - allowed him to succeed in his mission in becoming the Assassin of Time, resulting in Lavos' ascension and destruction of the earth, undoing the events of Chrono Trigger's original victory.
Schala, who exists in this timeline post-Chrono Cross (being post Time Devourer, she understands her connection to the Time Devourer and has some lingering pocket-dimension/time travel abilities) tried to manipulate time to stop Serge from becoming the Assassin of Time, but all of her efforts were in vain. She realized that the only way to save history is to entirely erase the Chrono Cross timeline and stop El Nido, and Serge, from ever existing. No Serge would mean no Assassin of Time... or so she hoped. So she travels to the post-Chrono Cross 2300AD, and before Balthasar establishs Project Kid, she stops him. She is still saved from the Time Devourer because the Darkness Beyond Time exists outside of space in time, so from a timeline perspective, she is already saved. The events there in destroying the Time Devourer still happened, despite the total annihilation of the Chrono Cross timeline.
And thus, the timeline is reverted to how we see in the PSX ending of Chrono Trigger. There's no El Nido, no Chronopolis... but Guardia still falls in 1005AD due to the mechanisms of Dalton. Schala, emotionally devastated for having erased an entire timeline and essentially "killed" billions of lives and the man she began to love (Serge), she removes herself from space-time in a self-made pocket dimension, where she crafts an ideal timeline for herself so she can live forever in a sort of paradise. A false paradise where she lives in Arni Village of El Nido along with a version of Serge that will never be doomed to become the Assassin of Time.
This is all backstory slowly explored in the game, some of which would have been done via flashback.
This new timeline, where the events of Chrono Cross never happened, is where the game begins, in the year 1200AD. During this era, the Republic of Porre (led by a Senate, although an unaging Dalton (due to his exposure to Lavos energy, along with Queen Zeal, in the Ocean Palace event) acts as a shadow ruler and really calls the shots) rules the world with a mostly iron fist, and it has "rewritten the history books" to vilify Guardia Kingdom and essentially remove their relevance in the history books.
The story follows Phase, a white-haired archaeology student from Manoria University. While on an excavation, he encounters a treasure hunter and rival, Toma Levine XXXIIX, and they find themselves in the forbidden ruins of Guardia Castle. There Phase finds the lost pendant that once belonged to Marle, lost since those horrible events in 1005AD.
Once they acquire the pendant, they accidentally open a Gate and after several misadventures, arrive in the new 2300AD. In this timeline, since Balthasar was convinced to stop Project Kid, he focused his energies to create the Chronoscope - a device that can detect changes to the timeline. He realizes that the constant time traveling has actually weakened space and time (part of the Assassin of Time's eventual/intentional plan), so he has decided to act as a sort of "police" to stop timeline incursions. His agents are Robo (the same Robo from post-Chrono Trigger, although with some upgrades) and the android Ada, who is this new timelines version of the Mother Brain AI. They are both PCs.
The storyline essentially has Phase and his allies (which eventually include Crono, Marle, Glenn, and Robo, along with several new characters) trying to stop these timeline incursions. We learn that each time Lavos "surfaced" (65 million BC, 3 million BC, 12000BC, 600AD, 1999AD) he released a elemental spawn that begins to affect that era in order to sow chaos and further weaken space-time. The end result: Phase, this new timeline's unknowing Assassin of Time, is forced to grow stronger by combating these enemies and gain strength, each time absorbing the essence of the spawn to become closer to his absorption back into Lavos.
The party is eventually forced to pull Schala out of her false reality, where she joins the party as the final party member. She and Phase clearly bond, as she sees much in Phase of what she saw in Serge (they both, after all, are artificial humans created by Lavos).
In the climax (equivalent to the events of Zeal in CT), the party arrives in 3 million BC, when humanity first touches the Frozen Flame, and Phase unknowingly acquires the last element he needs to evolve into the Assassin of Time. As he begins to transform into a biological, time-traveling monster and reabsorb into the Lavos of 3 million BC, he tries to fight it, but is seemingly unable. At the last minute, however, through the bond (and growing affection) he holds for Schala, he manages to stop the process just before it is too late.
However, Dalton swoops in and takes Phase's place, becoming an imperfect Assassin of Time. Dalton, having partially acquired the "essence" of Lavos is revealed to be the penultimate big bad. They then have to use the last act to reach Dalton and stop him from fulfilling his duty as an imperfect Assassin of Time.
Once taken down, the party stops Lavos once and for all... and this time permanently. They also resolve to ensure that there is no more time travel, because space-time is greatly weakened at this point due to all the time traveling shenanigans. The End.
In an epilogue, it finally reveals Janus (who has been absent the entire game), and sets up a potential follow-up in a new universe where time travel is all pre-determined fate, and allows for a sort of spin-off concept.
A few other parts of the story:
-Phase, who has been joined by Marle and Crono from 1005AD (pre-Guardia Fall), realizes that they can stop the Fall of Guardia and have a difficult choice in whether or not to alter the timeline and save the world from Dalton's evil Porre Republic, but at the expense of once again shunting countless souls to the Darkness Beyond Time.
-Lucca, who is an NPC working with Belthesar, has a crisis of faith. She realizes that she's seen all that science has to offer and begins to explore her spirituality (and whether or not there is a deity or Entity governing the universe).
-Frog is afflicted with a disease in 605AD, and the party resolves to cure him and return him to human form to remove the disease. This part of the quest is similar to Chrono Trigger's quest to revive the Masamune and is a decent chunk of the first act of the story.
-Doreen is revealed to be Marle's pendant.
-We also witness the Frozen Flame in 65 million BC, where it kickstarts its gradual manipulation of life on the planet in the name of Lavos. It interacts with both the remaining humans and Reptites and there are plot points aplenty.
-We learn that each Guru as an object of power: Balthasar has the Epoch and Chronoscope, Gaspar has the Chrono Trigger time egg, but what about Balthasar? He has the Forge, a magical amulet that allows him to turn literal dreams and emotions into personifications of life. It is thusly how he created the Masamune and Doreen (amongst other lesser Dream Creatures that are more animal-like in nature). Melchior kept this in his workshop in Zeal and it was lost when Zeal fell, so he never took it with him to 1000AD. However -- Dalton was able to acquire it from the ocean floor and used it to create his own Dream Creaturse and turn Porre from a protectorate of Guardia into a full-on military state, and using the Forge he was able to corrupt and steal the Masamune as seen in the PSX ending of Chrono Trigger.
I also started a second draft that made a lot of changes to this. In this new plot, which was never completed, most of the plot points remained the same: the concept of the Assassin of Time, Balthasar and his Chronoscope (and the risk of shattering space-time due to too much timeline interference). However, I shifted the villain a bit to introduce a character named Rouen, who was revealed to be Balthasar's vengeful son from further in the timeline. It also explored the concept of Counter-Time and Anti-Annihilation Energy, left unexplained in Chrono Cross.
In this draft, Counter-Time was essentially the ability to travel to erased timelines (remember, in the Chronoverse lore, when time is changed, the discarded timelines are sent to the Darkness Beyond Time and no longer exist). Thus, the characters were not only hoping through time, but were jumping to and fro on multiple timelines -- including:
-The Reptite timeline (had Lavos never arrived on Earth)
-The original Chrono Trigger timeline (with Lavos destroying the earth, before Crono and company save the day)
-The good timeline from Chrono Trigger (in which Lavos is destroyed)
-The Chrono Cross timeline
and
-The current timeline, which is a variation of the good timeline from Chrono Trigger (with Chrono Cross having been erased due to the Assassin of Time)
In this plot, Rouen was using Counter-Time to revisit previous timelines to learn how to become the Assassin of Time. He was essentially a spiteful son who hated his father's god-complex and wished to undo it all.