A script from that engagement would be hard to come by. The script that was published was the one that opened in New York before they did work on it and cut a few songs and at least one character.(The Persuasion and The Lusty Month of May and then bye-bye to Morgan LeFey.)
Alan Lerner wrote a memoir that included quite a bit on Camelot. It is called "The Street Where You Live" or something. Fritz Loewe may have also written one. Their secretary did too. Hers may be called "I Remember It Well".
www.abebooks.com
There are biographies of Moss Hart out there. Camelot gave him a serious heart attack that killed him within a year.
Camelot also split the Lerner and Loewe partnership (Fritz retired.) and gave Fritz Loewe a heart attack. Alan never really had a top drawer success on stage afterwards although he continued to write and had about 6 more shows produced. He also wrote adaptations for film and My Fair Lady is the only unalloyed hit out of about 5 tries.
The son of the man who was their agent/manager told me that one reason L & L wrote such great material was that Moss Hart and the agent knew how to play them off of each other. They would praise the other's work and that the one they were talking to couldn't possibly write something that equalled the other's.
And that is how you can get a My Fair Lady.
But they never really got Camelot right. To the positive is the score, plus a great first scene, last scene of Act One and last scene of Act Two. But then there is all the rest of that talk that gets in the way.
Maybe if Moss Hart had remained healthy, the show could really have gotten fixed right. I'm not the only one who has said that over the last 50-some years.
"If my life weren't funny, it would just be true. And that would be unacceptable."
--Carrie Fisher