If the loading is in the normal direction only, then use an axisymmetic FEA model. This will allow for a huge mesh increase. Make sure the mesh is to the point of ridiculous. To observe the correct behavior of Hertzian contact using an FEA model is extremely difficult. I gave up years ago when the results were not anywhere close to what I was being shown in my tribology class.
To save time as well you could replace the flat surface with a rigid wall assumming the sphere is alot softer than the flat plate.
Another option is to use the higher end FEA packages.
If it may be of use to you, you can define a stress plot and in the drop down choose CP:Contact Pressure.