OK, it is good we are getting contact, and the sub surface stress is something physical that is seen in these problems. You could change the contact behavior to symmetric, and change the pinball radius to a bit larger. The default pinball is a small fraction of the element size, so may try making it like 25% of your element size to see if that helps with the detection. You can do this by changing it to Radius, and then computing this value and entering it.
You may also change the contact detection to nodal projected normal from contact. Try displacement first, then back to force to see if these steps help with the detection.
You mentioned specifying contact stabilization damping, I would go back to that if this won't run and progressively increase until you can run with the force application. You then need to plot the stabilization energy vs stiffness to make sure is small. These are under solution information.
Keep in mind that the adjust to touch will change the physics of the problem slighly by offsetting the contact. While it works very well in many cases, for this case we don't want to be offsetting contacts any as that will change the shape of the bodies at the contact slightly, and if you are studying and trying to match analytical solutions, etc. I can potentially change the results a bit, so eventually, your final model should have this turned off. IMO.
Let's see what happens next. Thank you