Standard Earth Gravity point in the direction that mass moves (falls) so points in the +Z direction, which is downward.
Acceleration points in the direction that the mass is accelerating. In order to simulate gravity, you have to point it in the opposite direction, so use -Z as the correct direction, which is upward.
Plot Directional Deformation and you will see the mass moving in the wrong direction.
After changing the direction, here is the correct results at the end of Step 1.
Step 1 converged with the Nonlinear Controls all set to the Program Controlled and Stabilization turned Off. However Step 2 failed to converge, I need to look into that.
I see you have made a stiff material for the top rail. Since that has a different density, you can delete all the Point Masses and just use a higher density to achieve the correct static deflection. That will eliminate some of the warnings on multiple objects using the same nodes.