I don't understand what you mean by 'fancy swivel mounts'. Are you talking about RAM ball mounts? If so they make a couple of different shaped flat pads that can screw/bolt to the back of other mounts with a RAM ball growing out of the back of the pad. You use one of their female clamps (assuming the ball is considered a male) and one of the many RAM stationary mounts (handlebar, etc.). BTW, they make two length female clamps, a short one and a longer one.
If your gooseneck suction cup ends in a ball, you might be able to use the ram female clamp on that, but murphy is making sure right now your mounting ball is the wrong size.