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I have done a bit of investigating, and the noise that we see is because of the poor treatment of vertical mixing in the presence of a destabilizing heat flux.
Unfortunately, not only you cannot solve this issue by increasing the viscosity, but you end up also killing the eddies in the process.
Using a legit vertical mixing parameterization (CATKE in this case) solves the noise problem in the correct way and allows to remove the damaging horizontal viscosity.
In this PR I have also changed a bit the setup to have correct, faster and more accurate settings.
I do not know whether these settings are fully Reactant-compatible, so I have added the script in a new "forward model" file.
This is a snapshot of the surface u velocity from this PR