I don’t think May 3rd will be a problem at all. In 2004 I started on April 23rd and arrived at Kennedy Meadows on June 5 with 7 or 8 zero days. If you did the same schedule you would arrive on June 15th which isn’t a problem.
Regarding the water caches. Whether you start early, with the pack, or later you can never be sure of the water cache status. The last liter of water might have been taken by that hiker just in front of you and the cache won’t be refilled until the next day.
The best solution, and it does require advance planning, is to assume the water caches will be empty. Carry enough water to get you to the next reliable water source and know where you might find alternate sources farther off the trail if necessary.
Dehydration can be a serious problem in the desert. Try not to hike during the heat of the day (11-3) as your water requirements will skyrocket. Better to get up early (i.e., you’ll need your headlamp) and to hike right up to or after sunset. Try to cook at a water source (not a cache) no matter what time of day it is. You won’t have to carry your cooking water and can have a dry camp.
Yogi’s PCT Handbook has lots of other good information about dealing with the dry stretches of the PCT.
Radar