3D rotation to 90 degrees

You are just dealing with parallax and perspective. AE does not have an orthographic camera except in the Custom views. The only problem with that is that Custom Views like Front won't render. They will preview, but they will not render.

If you already have the keyframes set up to rotate the layers from 0º to 90º, all you have to do is press Alt/Option + Ctrl/Cmnd + 0 and set the layers to Auto Orient towards the camera. Then go back to the starting position and set the Y rotation to the value that gives you a straight-on view of each layer. 

Assuming you're just talking about y rotation, and the camera and the 6 layers aren't parented to anything, this y rotation expression should put the layer edge-on to the camera. So you could propably use this as your target y rotation in however you're animating the rotaiton depending on how you have things set up:

c = thisComp.layer("Camera 1");
v1 = c.position - position;
v2 = toWorldVec([1,0,0]);
a = Math.acos(dot(normalize(v1),v2));
radiansToDegrees(a)

AE only has a spherical perspective camera. The boards will never perfectly line up even if you use tricks like an extremely long focal length to minimize the curvature. As such you may want to use other methods like scaling the layers to create the illusion or an effect like Card Dance.

Mylenium