I think the issue is, are you trying to recreate the viewing experience of Cinerama on a 2D screen , or trying to create a 2D texture map, that would look correct if projected onto an actual Cinerama screen?
Sitting in a good seat at Cinerama, the image doesn't look compressed or much skinnier at the sides, because you turn your head to see it and you are looking at that curved section of the screen 'head on' so to speak.