It's not the score, but seeing it live can maybe give a few hints...

 

You've probably tried a number of things and I was going to suggest tracking down the availability of Ron Geesin scores. One of the main melodies within the piece is played on violin, you have the horn charts and some of the repeated sections are like a mini reprise. Geesin might have this all written out and maybe published and available to purchase. I would try that first. I would also attempt contacting him through the e-mail address on his official website. I contacted him in the past and he was very sincere upon getting back to me in a timely fashion and thanking me for appreciating his special talents. He knew I was interested in "Right Through" and "Funny Frown"..so he asked for my postal address, autographed the cd's and mailed them to me. He is an awesome individual.

The sections of A.H.M. that were originally created by Pink Floyd and presented to Ron Geesin by the band were mostlt improvised pieces. They were like fragments that needed to be surrounded by a few signature lines ..which is what Geesin did..however he more or less expanded further with intensity of a Classical mentality.  There is also experimentation towards the end with electronic sounding effects, percussion, mellotron and some in and out fading of notes sustained on horns. That could be a 20th century Avant-Garde style of improv I don't know? It is difficult to say that the particular section was written out as in comparison to a composer like George Crumb or John Cage where upon the average person might think their music sounds like noodling yet is charted out for 5 instruments and to be played exactly the same every performance. I mention all of this because Geesin and Waters shared a common interest in American Electronic composers like Beaver & Krause, Mort Garson, Ruth White and then several American 20th century Avant-Garde composers as well. It has been written in the past that the piece "Leave The Driving To Us" from Mort Garson's "The Wozard Of Is" gave Waters the idea for "On The Run". This could be true due to the fact that Geesin and Waters looked up to the American Electronic/Avant-Garde composers. Waters was experimenting with improvising sounds like Syd Barrett before him and Geesin was composing Avant-Garde string quartet pieces. Some of the transition sections from "Music From the Body" show that this was evident. There is a really interesting interview with Ron Geesin where he discusses the entire recording session of A.H.M. on Y.T. 

There is a BBC bootleg with an early live version of AHM. Comparing that with the studio version you can better appreciate the orchestral parts as there are no edits. 

The Italian cover band "Fluido Rosa" sometimes plays parts of it as they don't have the orchestra, but the two girls in the band (one is an excellent saxophonist) sing the choir. 

http://www.myspace.com/fluidorosaband/music/songs/atom-heart-mother-echoes-15924854" rel="nofollow - http://www.myspace.com/fluidorosaband/music/songs/atom-heart-mother-echoes-15924854

  

Off topic but I just had to say this. That band is awesome, their cover is incredible!

They have the drummer Derek Wilson who has played for Emerson

http://www.atominrome.com" rel="nofollow - www.atominrome.com

Blocked in US unfortunately. 

I can't read music so I don't know are they good or bad.