The paths Chrome/Chromium use to access policy keys in the registry are generated by
generate_policy_source.py, with the path constants in particular being set
here.
The easy way to change this is to modify the policy generation script to generate a different registry path for Chromium to look in.
Also, quick branding note that it would not be ok to use Software\Policies\Google\BRANDED-CHROME as a path, if you are not shipping something built by Google. Rather you'd want to use the path Software\Policies\BRANDED-CHROMIUM-PORT without "Google" or "Chrome" in the path.