I downloaded your model and opened it up to look for problems.
1) I agree with Erik's suggestion to cut the domain in half again and use a coarser mesh. The current mesh has 577k nodes, which greatly increases solution time.
I didn't cut the geometry in half, but I did use a coarser mesh, the one shown below has 50k nodes and solves in 219 increments in 28 minutes on 3 cores. Note in particular in the Mesh Details, I set the Defeature Size to 0.2 mm, the Default element size was set to 1.0 mm. The reason the Defeature Size is so helpful is that the geometry has some small features that I expect are just geometry mistakes that should be cleaned up such as this:
I left Standard Earth Gravity on.
On the next iteration, I would try to get 2 elements through the thickness of the base flat plate that only has 1 element through the thickness.
2) Put all faces on the symmetry plane into a Symmetry BC. You only have one face.
3) In Engineering Data, the PDMS material model fit to the data is okay but the error grows after 0.05 strain.
4) In Engineering Data, the Ecoflex 50 material model fit to the data is not even close. Try changing the material constant to improve the fit.
Set C10 = 0.6 and C20 = 0.001 and the model gets much closer to the experimental data.
With those material constants, the results are very different. You must decide which constants represent the material accurately.
5) When you want to share a project, clear generated data on the Model to delete the mesh and results so you get a nice small file. I don't want to wait 45 minutes to download a 13,400 MB archive. Here is a 0.4 MB file with the original material constants.