Groin discomfort - Saddle and aero position?

When I spend time at the drop (usually due to strong head wind), I shift my contact point with the saddle and put pressure at my groin area (which is not good for a long period of time). Bike shorts with thicker padding helps and shifting seat position from time to time helps but the situation still bothers me.

In order to avoid the pressure to the groin, should I get a different saddle (any recommendation)? Or should I tilt the saddle downward, moving it backward, etc? I don't know what I can do to make it work for both the upright and aero position.