I'm only using DT songs as reference, where ideally the "inspiration corner" is not a bunch of albums or half of the song structures of Images and Words, but their whole discography. I'm gonna cheat as well on some occasions, creating hybrids.
1. On the Back of Angels sprinkled with Bridges in the Sky
It's a difficult concept to explain, but what I'm trying to get is "a somehow standard opening song but with a bit of epicness thrown in". They had fairly "standard" openers (Pull Me Under, On the Backs of Angels, Untethered Angels, even The Alien which has a fairly standard structure and reaches almost 10 minutes just because of the solo), and sometimes big giant pieces like A Nightmare to Remember, The Glass Prison, In the Presence of Enemies which is part of a larger whole.... I'd like them to go halfway - yes, do a relatively standard song as first one, but without going overboard with the minutes, throw in some variety in the song and some bombastic epicness while staying in the "standard opener" realm, 8-9 minutes or so.
2. These Walls
Ideally the first single, a melodic, more simple song where they showcase their ability to create compelling melodies. Nothing too fancy, just a damn good song.
3. The Mirror / The Root of All Evil
An heavy song that doesn't go overboard with a million notes trying to prove they're heavy and edgy. Just a simple, effective riff and some menacing keyboard sounds from Jordan (The Mirror's keys are heavy AF) to create a good prog metal heavy song that doesn't try to out-Metallica Metallica.
4. Hollow Years / When your Time Has Come
The ballad-ish, guitar driven slow piece. I don't want them to write a song that actually resembles those, it's just a reference for something simple with a great chorus, I would have used Beneath the Surface also but the song should have full instrumentation and not just be an acoustic piece.
5. Home
I use this song as a reference for "the epic centerpiece of the album". They always had bigass closing epics, when was the last time the main song of the album was in the middle? we could argue about Lines in the Sand / Trial of Tears and which one is the better or "most important" song of FII, but just for the placement, Lines in the Sand is definitively an epic in the middle and so is Home, which I like way more than LITS.
Have the longest song of the album in the middle.
6. The Answer
The Astonishing had the most unique song structures of their carrer given the nature of the project. They wrote a short interlude 'cause the story needed it. What prevents them from doing a little short song just for the heck of it, in case Rudess or Petrucci comes up with it while doodling around on their instruments? if randomly a very short song pops up, go for it, don't try to embellish that section into another longer song!
7. Peruvian Skies / Endless Sacrifice
Something that starts slow and then becomes heavy. Two somehow distinct sections of the songs that work well together, with a natural and not abrupt progression from slow to heavy.
8. Erotomania but with vocals at the end
They'll probably do another instrumental, and if they do, I want something melodic with memorable and "hummable" parts, like Erotomania or even Dance of Eternity. Anyway, and for this I have no reference, how cool would it be if there'd be a sang "chorus" at the end? like their overtures (1928, Dystopian etc) there's a recurring theme throughout the song (more than one actually), for this imaginary instrumental I'd like for it to have a main musical theme, and at the end of the song, that theme gets actually a chorus sang by James.
9. Space Dye Vest / Far From Heaven
Time for another somber, moody piano slow piece.
10. A blend of Trial of Tears and Finally Free
Couldn't really decide between the two, I want the other epic, the closing one, to have a mix of elements of both: different sections, some acoustic / mellow parts (ToT has it at the end, FF has it at the beginning), a scenery painted with the music and the lyrics imaginery, lot of melody, and a grand finale.