The PRF model should work with *VISCO. I have used many different versions of the PRF model that way, and it does dissipate energy.
I don't recall if the PRF model works with *SteadyStateDynamics. I ran your test case using Abaqus 2019, and I get the warning:
***WARNING: VISCOELASTIC MATERIAL PROPERTIES ARE DEFINED IN THE MODEL. THE MATERIAL RESPONSE IN A STATIC ANALYSIS WILL BE BASED ON THE INSTANTANEOUS ELASTIC MATERIAL PROPERTIES.
Suggesting that it probably does not work (not surprising).
I also noticed that your material model contains an exceptionally many networks (20), and that the Sratio for about half the number of networks is basically 0. I would get rid of those networks.