Why did Ultimecia need to travel further into the past in order to Compress Time? This is where my theory comes in.

...

In this way, Ultimecia ensures that She is the source of her own power (to simplify things, she becomes both the chicken and the egg), so when the past no longer exists after time compression, it will not matter and she will maintain her powers.
But Ultimecia shouldn't by any means KNOW that her powers are a result of the loop. She'd simply think she got her powers from whatever sorceress was behind her in time, and that's it. She then want to compres time, not realising that it was her casting TC that led her to her death and to her powers being passed on in the first place. After all, had she known about her death at Squalls hand after casting TC, it would seem awfully stupid to go out and do exactly what is supposed to be the death of you!

It seems that Ultimecia needed to get further into the past for reasons we cannot hope to know. It might seem like a sad conclusion, but we'll never fully understand Time Compression on the basis of what we know, so this is one of those things which seems to only have the conclusion: she needed to be in the far past because that's how TC(time compression) works.

As for why Ultimecia can survive in TC and no others, you could think of the line of time as being the sum of every single particles personal histories. Since it is clear that Ultimecia is capable of controlling TC to at least a certain degree, she probably had TC start compressing every single personal history on the line of time EXCEPT her own. In that way she'd be able to carry on leading a normal life, while everyone else would be trapped in TC at Ultimecias will.

Your conclusion that TC doesn't ever completely finish is a correct one.
However, besides the things pointed out, your theory doesn't cover every thing. Ideally, the 'perfect' TC theory would fulfill these points:

1) Explain why we only see effects from TC at the point of Adels defeat and some time into the battle with Ultimecia. (After all, since TC would have certainly reached the events we play in the game prior to Adels defeat, we have to explain why we don't see any influence in those events).

2) Take into account the fact that you travel through TC and LEAVE TC before ending up in Ultimecias world, before seemingly entering TC again in Ultimecias battle. Prerably, it should explain why Odine makes it sound like you couldn't actually end up anywhere BUT Ultimecias time, when the error margin are VERY slim(considering how close Ultimecia comes to full time compression).

3) Take into account the fact the time in FF8 is static and set in stone.

4) Explain why Squall and Co were not affected by TC(ie. why weren't their own individual lines of time also compressed?).

These are the 4 main points. Over at www.gamefaqs.com we're actually in the middle of a debate on TC, and have succesfully created theories which explain almost all the unexplained elements, but not all points in an entirely satisfactory manner. We do however seem to be close to a conclusion, whether or not we conclude it is impossible or if we finally nail it completely. If you want to hear more about time and TC I'd recommend you check out the Time/Ultimecia Plot FAQ on Gamefaqs(search for Final Fantasy VIII, go to FAQs/Guides, and find the FAq called "Time/Ultimecia Plot FAQ; note that the one called Plot Analysis sucks big time). It's credited to my name, but ideally it'd be credited to everyone who has participated in the big discussions that have been on Gamefaqs for a long time.

Then, after you've read that, I'd recommend you catch up with what we're thinking today(the FAQ is outdated) by checking out the topic "Some things in this game make no sense". The TC discussion starts after a few pages. If you have some fresh ideas we'd be more than happy if you registered and partook in the debate.

If you don't want to read through the entire thread, which I guess might be understandable, I can post my most recent theory here.