The problem with this Armageddon Branch Theory is that the Black Omen transcends time and space and is connected to Lavos. Now we know from past theory on Lavos' pocket dimension that Lavos exists in a dimension that is connected to a number of timelines, and because Lavos' pocket dimension is not exactly inside nor outside the flow of time but transcendent, we see that Lavos will exist right up until the point where it dies, whether by natural or unnatural causes. Let's say Lavos dies of unnatural causes, ie, Crono & co. So, what we have now is Lavos' pocket dimension existing up to a point in time and then it disappears. Lavos and its pocket dimension are sent to the DBT from that point onward. So, what you see is that Lavos' pocket dimension ends up being transcendent up until a point and then the connection is severed.
Now, after all of this you may be wondering how this is connected at all to the Black Omen. The Black Omen works in a similar fashion, as it too transcends time and space. Now, if the Omen is destroyed in a certain time period, the connection, like with Lavos' pocket dimension, is severed after that point. This indicates the following:
1) If the Black Omen is destroyed in a time period other than 12,000 B.C., it will remain in 12,000 B.C. and following timelines up until the point it was destroyed because the Omen itself is still at least partially still in those timelines before it was destroyed. I am saying partially because of the transcendent nature of the Omen.
2) It is ambiguous as to what timeline Lavos is summoned from when the Omen is destroyed. We know the physical connection point that was severed with the Omen because we know what time period Crono & co. entered it in. What we don't know definitively is how this transcendent nature plays out when Lavos is summoned - Lavos could have been summoned from any time period the Omen was physically present in before it was destroyed. We know that this time period, however, had to have been sometime between 12,000 B.C. and 1999 A.D. because when returning to fight Lavos by using the bucket gate to 1999 A.D. from the End of Time, we see that Lavos' outer shell is damaged and defeated.
Now, my personal thoughts on this are that Lavos was defeated in 1999 A.D. The evidence I see for this is that when Crono & co. fight Lavos, the gate inside of its shell returns them to the End of Time through the gate contained in the bucket (they land right next to the bucket at the End of Time). While this could just be a game mechanic, it does suggest that no matter what route Crono & co. takes, the "when" of fighting Lavos is still the same - 1999 A.D.
