It will be hard to find enough people who each know all the cameras you have listed well enough to give you a definite recommendation.
I would like to help but I have only used the F11 and Z1 personally. While I like the compactness of the Z1, the image quality of F11 is way superior, and F11 has a better battery life (because of a larger capacity battery I guess).
Without knowing what matters most to you I would not know which one to recommend among the 2. Not to mention I would be totally clueless about the rest of the cameras in your list.
Have you read any online reviews? Care to explain a little more about the intended use you have in mind? Otherwise I doubt if anyone can give specific and relevant advice beside some generic coments about the cameras.
Frankly speaking, I haven't read up much about all these cameras, with the exception of the Fuji F11. I haven't used it before, but it's pretty spiffy being one of the few (or perhaps the only one, besides its sibling, the F10, and the new F30) compact cameras that handles well in low-light situations, taking decent photos without flash, and handheld.
to get a better idea of what your needs/ wants are and what sort of camera would suit you best. Alternatively, if you wish to up the stakes and spend upwards of $800, I'd wholeheartedly recommend the Canon PowerShot S2 IS. That said, look into other superzooms by competitors as well.