Nicer shorts might feel better. They get kind of expensive though.
And I cannot imagine how cycling shorts would give you pain in the perineum area when without them you don't have that pain. From your description of how your sit bones hurts vs. you perineum hurts, it sounds like you are sitting differently depending on what you are wearing.
Make sure your cycling shorts are on tight. Some people complain that the chamois pad bunches up and feels like a diaper, but that isn't pain, just really weird feeling.
Bibs also help because they will hold you shorts tight so they don't have the ability to bunch up.