Here you go with all the hyperelastic curve fitting constants:
C01: -1543725.306, C10: 3478878.725
C01: -4325191.035, C10: 5952426.9831, C20: -97843.705
I would prefer to use Signorini as the fit is quite accurate, may be not for lower strains but later for higher strains. Please also ignore the added 1 in strain values. This is normally done in order to get the results at zero or low strain. Please see Hyperelastic material documentation for more info.
Can you also please tell us about this material? It will help other users to use this data in case they are looking for same material type.
I hope this help. If you need anything further, do let us know. We will be glad to help.