Here is the linear material, which has an 11.6 Hz natural frequency, delivering the expected isolation:
Looking at the plot in the paper shown below, I don't think the authors in that paper are starting the base excitation after gravity has dropped down the mass. I think the mass is falling to the equilibrium height at the same time that the base is vibrating. This makes the simulation easier, since I had to create a 3 step simulation to first let the mass settle to the equilibrium height, then start the base motion. But experimentally, that is an odd setup. It means the mass must be supported so that the springs are not compressed and the mass is released at the same time that the base motion begins. Don't you think that is an odd way to run an experiment?