As you can see from your neutron fluence scoring by USRBIN, the forward direction is indeed favoured.
This is fully consistent with the USRBDX output, where you read the flux integrated over the solid angle, while what one expects to peak in the forward direction is the differential flux dN/dOmega. The integral is naturally affected by the fact that the solid angle in the forward direction is significantly smaller, as input in your USRBDX cards.
Moreover, USRBDX does not appear to be the right choice for your purposes, since the angle of the neutrons leaving the target through the lateral surface is measured with respect to the radial direction (normal to the surface) and not the beam direction. USRYIELD would allow you to get the neutron angular distribution dN/dOmega, as a function of the polar angle wrt the beam direction, with a single card instead of eight.