Is it possible that the contact has Trim Contact enabled? I would delete the contacts and recreate them from scratch.
You could also try Explicit Dynamics. In the video below, the body-interactions are frictionless. I also removed the frictionless support on the right end of the rubber since that is not present in the full model. After I played this animation, I plotted normal stress in the Z-axis which is Hoop Stress, but did not see a compressive stress building as the rubber moved closer to the axis of revolution, so now I want to investigate why that is. You may want to do a small test for yourself before you spend a lot of time on this solver.
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