The derivative of CalibratedStereoCamera.project:

H1=(1/z)(({{1, 0, - xL/z}, {1, 0, - xR/z}, {0, 1, - y/z}})).(({{0, -z, y, -1, 0, 0, R00, R10, R20}, {z, 0, -x, 0, -1, 0, R01, R11, R21}, {-y, x, 0, 0, 0, -1, R02, R12, R22}}))//FullSimplify//MatrixForm

To get rid of (1/z) factors, work in terms of u=x/z and v=x/z.

H2=(1/z)(({{1, 0, - xL/z}, {1, 0, - xR/z}, {0, 1, - y/z}})).(({{0, -z, y, -1, 0, 0, R00, R10, R20}, {z, 0, -x, 0, -1, 0, R01, R11, R21}, {-y, x, 0, 0, 0, -1, R02, R12, R22}}))/.{xL->z uL,xR->z uR,y->z v}//FullSimplify //MatrixForm

Finally, avoid divides.

FullSimplify[H2/.{1/z->d},{z d ==1, d x == uL}]