I just wanted to update you with some new information. I went ahead and purchased the Casio EX-P600 after all, despite my concerns about the flash intensity, and I am very happy with it. The flash intensity is not a problem. The spec of 9.5 feet range is actually the same spec as my older Nikon Coolpix 775. But the flash on the Casio is much better than the flash on the Nikon. Not only does the flash reach farther, but it is much more evenly distributed.
With the Nikon, when I took a flash photo of a group of people (like say 8 people sitting at a long dinner table), the closest people were very overexposed, and the farthest people were too dark to see. But with the new Casio the same shot turns out great.
Oh, a Casio Customer Support rep told me that the "Strong" setting on the flash does not actually make the flash brighter. It just makes the flash stay on longer.