Like A720 IS-but shorter flash recharge time?

I want a camera that is just like the A720 IS (8 mp, great image quality, fast non-flash performance, optical viewfinder, low purple fringing, 6x zoom), but without the long flash recharge time. Is there a camera out there like that, or will I have to just get the A720 IS and live with it?
Also, what exactly is flash recharge time? Is it the time between flash shots, or is it something else? One place I heard that the flash recharge time is 8-10 seconds, another place I heard that the shot to shot time with flash is 4 seconds. So is flash shot to shot time a different thing from flash recharge time?

You're starting to venture into territory where you need to step up to an DLR if you want better performance. Compact cameras like the A720 IS are very powerful - for compact digital cameras. But there's a reason why people buy digital SLRs instead. Flash recycle time is going to be a problem with any compact digital camera.

There is a difference between shot-to-shot time and flash recycle time. Depending on where you saw the numbers, the shot-to-shot time should be the time between shots, with the flash off. Flash recycle time will be the time it takes to shoot two consecutive flash photos.

Another option is to look at compact cameras that have a flash hotshoe. I believe the S5 IS has one. If you mount an external, hotshoe flash, then the flash isn't limited by the battery and electronics in the camera. The Canon external flashes all have much faster recycle times than the compact cameras.