You got rid of the singularity when you changed the sharp corner to a radiused corner.
Now you have Hertzian Contact Stress, which is not a singularity. I don't believe the stresses will keep increasing without limit as the element size gets smaller and smaller. I believe you will be able to plot a mesh convergence plot showing a converging trend line.
Please reply with a table of stress versus element size for the model with the radiused corner.
Also, you only need small elements over a small region near the contact point. Sizing with the Sphere of Influence is a good way to get that effect, but you have to create a Coordinate System at the contact point first.