You were doing so well in explaining it, too.
THE GAME IS NOT STUCK IN A TIME LOOP.
Adel was the previous big-shot sorceress that ruled Esthar with an iron fist and put it at war, Laguna tricked her into entering a previously-prepared chamber that contained her powers and sent to space with the Ragnarok. Years later, Edea had sorceress powers but kept quiet about them(not everyone is an OP Sorceress, the past ones you fight prove this, some can only cast Fire). Squall ends near her with Ultimecia dying, the power form Ultimecia jumps into Edea, Squall tells her to make Seed and go back to the temporal rift.
After Edea is defeated the second time, Ultimecia stops possessing her and possesses Rinoa instead. She uses Rinoa to remove the seals that kept Adel back and leaves her to die in space, possessing Adel(to whom the Sorceress' power passed to after Edea) instead.
They Laguna has a stupid plan and everyone uses Rinoa as bait, defeating Adel with brute force to force the power back into her. Ultimecia then controls Rinoa again, and Ellone sends boith Rinoa's and Ultimecia's consciousness as far in the past as she can(which was what Ultimecia wanted to start with: the only reason she's at this point in time is because the machine she's using to send her consciousness back can't go farther than the game's present).
Thus Ultimecia starts doing the time kompression, and Ellone cuts Rinoa's and Ultimecia's conection to the past, slingshotting them both to their respective times. The time kompression couldn't be stopped, but was delayed long enough for them to cross the mindfucked/sciencebabbled landscape, crossing space to cross time or some such. The party is warned they'll disappear if they end in a timeline where they don't exist, so they have to believe in THE POWER OF FRIENDSHIP(not kidding)/eachother so they can avoid being deleted from existence.
They finally get into Ultimecia's castle, beat her, Ultimecia uses her powers to animate the concept of "the strongest being that can exist" straight from Squall's mind to create Griever, you beat both of them, they fuse, you beat them again, she transforms one more time just as the time kompression is finishing(at this point everything stopped existing except you and her, and if you get ko'd she can absorb your characters too). When she's defeated for the last time, the time starts to uncompress and everyone gets lost in the rifts of time.
The party ends up thinking of the same place where they wanted to exist together, the orphanage. Two people are missing though: Rinoa since she wasn't form there and Squall, because he really didn't do the whole "power of friendship" thing. They promised to meet in a meadow, but Rinoa is there alone. Cue Squall being erased from existence and losing his memories even as he try to remember Rinoa and she's waiting for him(ending sequence, also the starting one), he doesn't manage to, she uses her Sorceress bullshit powers to first give him a second wind, and then to leave breadcumbs with her own memories for him to find.
With his second wind Squall remembers the orphanage as well, but gets there in the wrong part of the timeline, with a much younger Edea. This is the first part where he meets her, and tells her about the Sorceress and Seed. He then gets lost again in the temporal rift, following Rinoa's breadcumbs/sorceress bullshit/memories/feathers until he appears next to her in the meadow.
Cue good ending, everyone is happy, etc.
But wait, Ultimecia will rise again!
Yes she will, but her world wasn't barren in the first place, everything we know is that she was strong as fuck, and had a fortress near the orphanage. She'll rise in power, go back to the past, be defeated and die when the time comes. Since she's from much further in the future, Squall & co. are probably dead even before she's born, so it's not their problem. They got their good ending.
There's one catch though: the sorceress powers are lost forever. Why? because THEY are stuck in a time loop. Ultimecia>Edea>Adel>Rinoa>Ultimecia. After Ultimecia dies(in the future), there won't be a Sorceress ever again.