I would like to interject some thoughts along this line of reasoning. Forgive my lack of scriptural references and feel free to refute, but this come to mind and I wanted to share it before I over thought it and started picking my own thoughts apart and then talk myself out of posting.

I agree that it is hard to think in a multi-dimensional fashion so I tried to draw upon what truths I might be able to see in this line of theorizing. Theories are subject to current understanding and the term theory is often misunderstood. Theory can be observed, but theory can also be a projection of what appears to be possible.
Observable theory has this quality "It works this way, but it may not be the only way it works"
Projectional theory is based upon non observable possibilities that have not been proven to be false, but have not currently demonstrated any value to change anything we observe.
Projectional theory should never take the place of observable theory as fact but as possibility. These are my thoughts on how science should explain how theory actually affects us, but unfortunatly it rarely is.
Now, the thought of going sideways in time intrigues me enough to contemplate it with the following thoughts. Some of the links TB posted on Free-Will actually refutes the "Term" of free and reduces our will to the ability to understand, which is more along the line of what scripture tells me. Please do not focus upon our disagreements of this and read the rest of what I wrote.
So, at the risk of opening that can of worms I simply do not reconcile a choice with being free in a biblical sense. As I stated earlier the analogies of our human existance such as free people or freedom of or from something are not really applicable because the source of our freedom or lack thereof is a sovereign God that is intent (however he does it) on getting us where ** Edit
HE wants us to go that is scripturally a place that is against our will.
With that said, taking that risk, I propose the following.
I fully reject the idea that Gods word changes, I think the idea of multiple timelines is not a reasonable cause for Gods word ever changing. However, God word can be built upon. Meaning in other versions of history there may be more or less knowledge about God but not different.
If ALL comes out of God and God is in ALL then Gods spirit manifests the entire scope of ultimate existance. There is not a different God in a different time line. Because that WOULD be a changed God and a God whos word is different would have to be a different God.
We misunderstand the phrase "ALL things are possible" because we can propose illogical instances about God that cannot be possible that do not detract from Gods sovereigty. So proposing an impossibility with God is not an unreasonable proposal when that impossibility is simply the nature of existance.
God is LOVE so would it be possible for God to transform to HATE? We can speculate that he could, but he doesn't, so we can go down that trail, but I think it is simply impossible as much so as the argument for God making a rock so big that he could not lift it. Illogic is still an impossibility.
Here is a verse that supports that.
1Corinthians 1:25 for the stupidity of God is wiser than humanmen, and the weakness of God is stronger than humanmen.So it really does not matter what we can speculate on there is nothing that can be used to say that man or any other being has any chance of being more powerful than God.
So continuing on I can see a possible sideways movement even within my own life. I will give this example, in fact I have always been wary of telling people this, mostly because the reactions have never really helped to validate it and I have only had to hang onto what I know God has shown me. So I am glad for the thought process that this thread has caused. As it actually helps to validate more of what I know.
Multiple time lines all intertwine and I think separate versions of history is also linear thinking, if one timeline cannot affect the other then there cannot be sideways movement and therefore cannot be non linear onlt multiple instances of lineararity (is that a word?) haha. It actually is a intellectual cluster saying "I get a Do Over"
I think intertwining multiple time lines cause a closed loop that increases who we are as we go along.
When I was within my drug addiction I can look back and actually see that I was much happier than I am now concerning how I felt, but I did not see what I was doing to those around me. I lost friends, alienated family and hated people but I was happy. Christians will try to claim that you have to be miserable in that life and they have
no idea what they are talking about. If I had died during my drug use I would have died happy, period.
I have much more turmoil now that I am
AWARE of being on a path being drawn to God. From physical birth we are being dragged by God whether we know it or not. There are no choices that I made that I willingly made to "change". I used drugs in the firsty place out of a compelling feeling to belong. I stopped through a compelling notion that my wife was preganant and it was something I shouldn't do. People invent the free will action after the fact of something because they want to feel in control, thats all that is.
I do now willingly refuse drug use because of what I was taught, but that teaching was not of my own, there is no argument for free will that will tell me differently than what I know in my own life, that is why the "Term" is wrong.
Where I see the truth of multiple time lines is that I think there is an intertwining of physical reality that God has built for us. SEE, we misunderstand reality and the physical in the first place. If there are multiple version of history all going on at the same time, then the plane of existance that they are in is still physical.
I also sense that the multiple versions work together for our correction to build upon what we know. My past drug use is taken by Christianity and made to be this beacon of death and is made to remain a dark part of my past, my sin is taken and shaped to be a constant reminder of the possible doom I once faced.
What if the correctional value of multiple time lines has reshaped time so that my past drug use is "not remembered" as a negative and integrated into time as a redemptive value of an experience that humbled and shaped me towards the image of God.
I say that because in my life it is entirely true, I have countless example of positive things that only are taking place in my current "time frame" because of my past "sin" but I do not see it as shame I remember it as good.
Hope that was worth reading, LOL