Odine speaks of time as being something one can move forward along. How can that be if it's all an existance-at-once, which is, again, what Ultimecia was trying to achieve by combining "various states of present" as the Tutorial calls it?
You missed my point. Perhaps I didn't portray it clearly enough. What I mean, is that the future isn't 'waiting to happen' as it were, it's already there. So even though Squall and Co haven't witnessed the future occur, people from the future can still come from the future into their own time.

Time compression would make all time exist at once in the same point. I am saying time exists all at once but in the natural line form. To make an analogy, take the line of time to be a road, and people on it as cars driving along the road. What I am suggesting is that this road didn't start off empty, for the cars to then start driving down it. I am suggesting that the road came with the cars already on them.

So if we were to look at the road from a birds view there'd be cars travelling in a continuous infinite stream everywhere on the line of time. Everything's happening 'at once' but not at the same point in time, as it were. Hope I made that somewhat understandable.

When examining it in the present, yes, it would look like things always were that way, with a being from the future somehow being present in the past long before they should have been alive (or when they should have still been a toddler depending on your point of view in regard to another matter).
This is what I mean. I just believe this would be the case since time first begun. Time would be literally set in stone from the very beginning, so we could zoom in on any point and watch a row of events before switching back to a past far in the past and observing that instead.

While Ellone said that one can't change the past, the People she used to try to change Laguna's past never attempted to subvert Laguna, Kiros, or Ward's will to their own, unlike what Ultimecia did in regard to Edea and Rinoa, the future Sorceress having an objective and intending to take over those who she possessed.
Well, this is simply a disagreement on what degree of importance Ellones statement should have. It's true, that technically speaking, Ellone doesn't necessarily know the truth based on what she does in the game. However, I firmly believe this was Squares way of letting us in on their interpretation of time in the game. It ties up that entire plot point, sets the scene for Squalls subsequent attempt to save Rinoa and fits in perfectly with the implied notion of fate. Fate(in conjunction with Ellones statement) would for me imply a nonchanging line of time, and that rules out any original time as far as I'm concerned. The alternate explanation I have presented is the one I have then taken as being the most logical.

Of course, I understand that you may disagree, but I am certain it is not because of a fallacy in my argument, but rather in core differences of opinion.

While it's true that Ultimecia doing this resulted in the present and future (for Squall and the others)/past (for Ultimecia) that has to take place, to say that it would be impossible (based on Ellone's abilities) for them to have changed anything is false due to the fact that Ultimecia could subvert another's will while in their mind, using the device developed by Odine that simulated Ellone's own power, but which apparently isn't as powerful as hers due to it not allowing Ultimecia to reach as far back in time as she needed to in order to cast Time Compression. If Ultimecia could do this, why could no one else?
If time was set in stone, nothing Ultimecia did while possessing anyone would be changing the past, it'd simply be another event set in stone.
So it's only false if you believe the past can be changed, which brings us back to cardinal differences which aren't answerable in the game(on a factual basis anyway).

It's this concept of the same People making the same choices everytime because they're the same People that allows the timeloop itself to remain intact.
Or much simpler(in my eyes anyway): the timeloop remains intact because you can't change the past.

Without establishing a loop with no breaks, it's theoretically impossible to permanently change the past.
I don't see why this conclusion is drawn. There certainly isn't any basis for stating something as 'theoretically impossible' in such a discussion. Perhaps 'theoretically impossible' within the framework of your interpretation of time.

To summarise: Whether or not the line of time is changing or not isn't a question that can be logically concluded from ingame information. My own view works out perfectly logically, and I see it as the most logical. Your own view is that an original time is necessary for it to all start.
I haven't been in any way convinced by your arguments I'm afraid(doubtlessly goes both ways), so unless you can point out any logical errors I won't change my opinion here.