Here's the list that a friend put together of some essential bands, tracks, albums of Post-Rock.
https://rateyourmusic.com/list/TheParkA ... ost_rock_/Post-Rock shares some of the characteristics of Progressive Rock for a new generation but with all the wankery and solos gone. Often a lot more stripped down sound obviously.
Pink Floyd is a decent example of where some of this came from. Probably more in common with early
Krautrock so definitely consider you can find some cool records from Germany in the 70's that were along the same lines.
What I'd recommend checking out:
Talk Talk's - Spirit of Eden & Laughing Stock are considered pretty essential and really starting points from that sound. Not a bad transfromation from a band that started as just a rather good new wave band.
Slint - Spiderland is also considered a classic album and is where Math Rock (with very unusual time signatures) really split off while remaining a part of it still.
Drive Like Jehu, Shellac, and Polvo are worth checking out if you go off on that tangent. My favorite of the later era of Math Rock has to be
Battles. That's a great bizarre little album.
Definitely give
Sigur Ros a try as they have quite the discography and are well regarded from that scene. With the language barrier (a lot of their songs are in foreign language or using the nonsense type of language (made up sounds) that
Cocteau Twins (Dream Pop) used to do when they started. To some like me that's real distraction and turn off, its not as big a deal to some people.
You've already mentioned
Godspeed You! Black Emperor & Explosions in the Sky and they are definitely at the top of the recommendations list.
Mogwai and Tortoise I'd have to throw in there as well as being exceptional Post-Rock bands.