Nice area of research!!.
I find some discrepancies on the data and your model.
Your final thickness is 2mm in the pres-stretch step1.
That shows some issue in the compressibility. It should be 0.16mm or close as advanced on the paper.
Your analysis should consider material nonlinearity (Mooney Rivlin) not only geometric nonlinearity.
Hint to check the accuracy of your results: This is a Pure Biaxial Stretch (in cylindrical coordinates).
Principal Stress 1 and 2 must be equal and uniform and third negligible. Image on the right shows your VM stress field.
Minor comment: A principal Stretch of 3.5 delivers a final radius of 200mm not 195mm.You could do some small adjustment here.