SPOILER ALERT
Do NOT read this is you don't want to know anything about the Rocky IV Director's Cut before seeing the movie yourself.
I saw the Fathom Events showing of the Rocky IV Director's Cut at a theater near me tonight.
As for Survivor's music in the movie.... Sadly Man Against The World is still NOT in the film in anyway.
Burning Heart is still in the film in the normal spot.
Eye Of The Tiger was moved from the beginning of the film to the end of the film. It is played after Rocky finishes his speech to the Russian crowd after he has just won the fight, and it is continued into the end titles.
A very small clip of the song "Sweetest Victory" is in the film early on, but it's a very short clip and it's largely drowned out by talking and crowd noise.
I liked the film a lot. I won't go into details as of now unless anyone asks me questions about it.
I will say that it has several scenes that I think should have been in the film all along.