If you consider that originally Illumination Theory was going to be the second track and was changed to the last in the last minute, it's kind of a weird "overture" to that too(not really though). That's the main difference between these and the other instrumentals, although I think I already made my point before
Cripes! I really couldn't imagine that... and then I played them back to back, and they really do flow very well indeed. Although The Enemy Inside was absolutely the right way to kick in, Illumination Theory is... surprisingly coherent, as the beginning of a ride, and the back-to-back flow from one to the other is brilliant. Works much better at the end, the big symphonic bit feels more "earned" at the end of this huge sixty minute odyssey, but I'm genuinely astonished at how well it still fits in pole position. I wonder how the rest of the album was to be structured.
[ETA: Funnily, having just finished the song, the one bit that really does suffer when you pop Illumination Theory at the start of the album, is the instrumental section in The Pursuit of Truth. At the end of the album, that's earnt, especially after they've spent fifty minutes being curt, but at the beginning, it feels like it's stalling, when you really want an opener to get to the point. I can totally imagine that final chord giving way to The Looking Glass, though.]
That's no reason to dismiss FAS as a proper instrumental, though - they didn't move it when they shifted Illumination Theory, it's totally its own statement. That's not me saying you're wrong, it's me saying I don't get it. It's not only a DT instrumental, I think it's an incredibly strong DT instrumental.
I wonder what would've closed the album then. Nothing else from it is strong enough to close the album IMO.
Maybe that's why they wrote the Easter Egg? Alternatively, JP always said he imagined The Bigger Picture closing a live set, maybe The Enemy Inside was in the middle and TBP was at the end? You're right, there isn't another obvious closer.