I did the Kautz in mid-July of 2002. We found that camping about 1K below camp Hazard both easy going on the first day and allowing for a good position on the summit day. We took a siesta day there --- very relaxing and good for acclimatization. From there we departed about 1 am (at the latest) and quite literally jogged through the icefall. If it is warm (as it was in July) MOVE through the icefall, summit early and get down early. We descended through the icefall around 10am, enjoying great 55 degree AI in the gully.
cheers.