I don't have your camera, but I do have two older Exilim cameras.
In any of those best shot modes, do any of them have additional options on your screen that allows you to change additional settings?
For example, on my EX-P600 in Fireworks mode, there are two addtional options that pop up on the right side of the screen. I can now easily control my aperture and my shutter speed by pressing the directional pad.
Of course on this camera, I have full manual mode so I don't mess with these best shot settings, but it's there for you to mess with.
