The design I am now aiming for is shown below. The first cylindrical lens has a focal length of 230 mm. the second lens a focal length of 75 mm.  This should reduce the cross scan error and make the beam more round.

A side view and top view are shown below. ( the cylinder lenses are drawn incorrectly the curved side should face the bundle)

Note, this is different than the technique used in reflective polygon scanners where the collimated bundle is compressed to a line and after reflection is expanded to an ellipse, see patent.