Where are you getting your instantaneous shear modulus from? What I was suggesting is that the G0 (instantaneous shear modulus) in the equations that you shared should be the peak shear modulus from the time-dependent shear modulus curve. Even if you're getting the G0 value from some other experiment, use the max. value from the curve for verifying the fit since the G0 value that you may have from other experiment is not used during the curve-fitting stage.
Regarding the data, what you have is sufficient to define the viscoelastic material. The instantaneous shear modulus and the Poisson's ratio must be input under Isotropic elastic properties and the normalized relaxation constants and their time constants under viscoelastic behaviour.
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New Post - Reply To: alternative to curve-fit (Prony)