This one is hard for me because I'm not much of a music guy, and your no.1 list has some difficult criteria (like pushing the limits in what sense? Jumping over the capabilities of the console? I'm not sure how to quantify that in music terms).
Let's give this a go:
1.-
Liberi Fatali, from Final Fantasy VIII. The first time ever Nobuo Uematsu went experimental with chorus and orchestra on the same piece (though chorus had already been used before for One Winged Angel)
And going with everlasting, amazing main themes, there's also the main theme of Metal Gear Solid 2 for the PS2, which is absolutely fantastic:
Can't really think of any meaningful third OST that pushed a system to its limits.
2.-
Birth of a God, in Final Fantasy VII. This one generally gets extremely overshadowed by every single other battle theme, and it doesn't help that it comes right before One Winged Angel, but it's absolutely superb.
Persona 4's Corridor provides a much welcomed change of pace in terms of music, especially how vibrant everything else is. I rarely ever see anyone talking about this particular piece.
We'll be dead in Ten, from Call of Duty 4: Modern Warfare. Rarely I see people discussing Call of Duty's ost, and generally Modern Warfare 2 take reign over those. Coupled with the fact that people generally go traditional with escape osts (think Warthog Run from Halo), it's a shame that this particular piece is always so largely ignored, as it is probably the best one I've heard as far as making a desperate escape goes. It fit so incredible well while playing, and it's so damn great listening to it even without context:
3.-
If I have a profile page and I want people to feel welcomed, I guess we can go with something like The Fragance of Dark Coffee, from Phoenix Wright: Trials and Tribulations. In this case I'd add the jazz version, for extra edge in the taste:
4.-
For no particular reason, Shadowlord from original Nier.
