Is it possible to simulate scattering with the proton at rest (i.e. PBEAM=0) ?

Answer:
YES for the elastic and quasi-elastic processes, where kinematics and matrix elements are calculated in the center-of-mass system of ep.
However, NO for the DIS process because parton momenta are calculated using the Bjorken-x as a momentum fraction.
When you simulate scattering with the proton at rest, first you have to calculate in the center-of-mass system of ep, then transform the results into the laboratory system with the proton at rest.