Well for me it is important who did it because we do know the views of people and thus it could have only truly been Varis or Elidibus. Also there is no indication in the bad future that anything had happend with Varis, because I do believe that the death of an Emperor would make changes. Like you said it could very well lead to civil war. Would Garlemald still fight in Eorzea then? The future did make it sound like the war was still going on which imo makes not much sense if one country has problems on the inside. Thats why I believe that the bad future had played out quite different thus we already changed most of that anyway.
Is it still primed for rejoining? I really got the feeling that we stopped the rejoining by simply destroying the lightwardens. Because with no Lightwarden left, the huge amount of Light is gone and most sineasters will probably be dealt with soon enough. The exarch being ready to send us all back indicates that the danger had passed. And Emet wanted to use us as the most powerful sineater to start the rejoining again which hints that we did stop it by killing all the wardens.
Eden itself is only a side story not main story. And its not there to stop any further light but to bring back more land to the first. Theoretically as far as we know the first could have still continued on with life just with 90% of its land gone. There is imo no indication that the flood of light ist still happening right now. Otherwise it makes no sense that Elidibus would give up the body of Zenos that easily. He probably sensed that we changed the first and killed Emet thus knew that the flood was stopped.
I thought that him believing that he would cease to exists hints that he too thought that only one timeline exits and that us changing it would mean that he will be gone because "he" as the exarch will not come to pass. Which also makes it a great sacrifice on everyone that was living in that bad future (but it seems like the world was doomed) because they too would cease to be. Him still being there could hint at a lot of stuff. That could mean that the bad future can still happen but as I wrote quite much already, I doubt that. The whole story just feels that we have done the impossible and changed it. I just cant see how the stuff would still happen in the bad timeline, especially with the scions still stuck on the first, Elidibus not being Zenos anymore and Zenos being against black rose. Also the first would need to be plunged into another state of rejoining.
There could also be the chance that your theory is true and there was a split and the bad timeline will continue to exists as a side line on itself, which means that Graha was wrong about how timelines work, everyone will still have to suffer on that line and it also just leaves my head spinning. So I hope that this is not correct and the exarch is just a huge paradox that should not exists but does so for reasons.