First of all, I am not well versed in Chrono Trigger fanfic, so I thank you, Acacia Sgt. I only read one chapter and it seems to be an interesting idea, so I'm going to have to read the rest of it. Even if it doesn't develop in the way I think it would, I like to see alternate views.
Zipp, I find it interesting that you brought up the other time periods in which Janus could have landed, and I find the 2300 A.D. scenario you outlined very compelling. It would be interesting to see what affect this would have on his mental and physical development, as it is an open question as to whether it would provide him with empathy or only make him even more bitter and solitary than he eventually became. As an "enlightened" Zealian, would he see the condition of the world as a wrong that would need to be fixed or would the ruined state of the world be the inevitable outcome of messing with Lavos? Would he leave the world to its own devices? Would he see his fellow humans as survivors, or as dirty Earthbound people?
As some of the other posters insinuated, though, I doubt he would have been able to develop his magical talents as well as he did in any era or setting without the Mystics (the only other natural magic users). As much as Janus used the Mystics, they undoubtedly taught him techniques or at the very least helped him refine techniques and skills. I don't believe even a prodigy can live up to his potential if he doesn't have an environment to help him improve. On the other hand, with 2300 AD at least, the enemies are actually weaker than they are in 12,000 B.C. (and some parts of 600 A.D.), although how much of this is a gameplay function or how much of this is canonical to the story is up to debate, so it's possible he more than hold his own. But in the future, the best he could do is go around killing Lavos spawn. Maybe he'd fight Mother Brain if he were to become attached enough to the human cause, but I doubt it.
That being said, I do agree that Janus is very adaptable, and I am not optimistic enough to believe that Janus would become a completely well-adjusted person no matter where he was deposited (although I'd argue that at least some of his unpleasant disposition was due to him being pampered). However, the form that the manipulation would take and the lengths he would go to would differ based on what he had available to work with. The question is do the other time periods have other races or groups who would possess the skills he would need to actually summon Lavos. In the game, we aren't shown any other groups who would be capable of doing so. Only in Zeal are there magic using humans, only in 600 AD and 1000AD are there Mystics, and only at the End of Time is Spekkio. Of course, it's possible that there are some unseen groups that have these abilities, but working from what is presented in Chrono Trigger, it doesn't seem likely that he'd be able to even work toward getting revenge. Since that's his primary motivation for most of the game, it makes me wonder what he would have done if that option were taken away from him, or at least made less accessible.
Now there is the question that if Janus has not been aligned initially with the Mystics, could Lavos even have been stopped? After all, while Crono, Marle, and Lucca learn about Lavos in the future, it is only when they are deposited in Medina that they find information that leads them to think Magus is they key to stopping The Day of Lavos. If Janus were to appear in other location or at any other time (except perhaps 20 years before 1,000 A.D. in Medina -- I can see him leading a second insurgency that the heroes learn of, then attempt to stop him), then how would they learn about Lavos to stop it? If the entity made a gate to 12,000 B.C. and deposited the party there, they could learn that way, but obviously there'd be no Magus or Prophet there if he wouldn't attempt to summon it in the first place, which leads me to wonder how differently the game would have developed. Would there have even been a need to go back to 600 A.D. or even 65,000,000 B.C.?
Edit: I attributed the wrong posts to the wrong people.