It's still a little bit of a climb. You can get water above Trailside Meadow at the creek you cross just before you get to the slabs above Consultation Lake. (I don't see it listed on Bob Rockwell's list, though I've personally never found it dry.) But I'd just take the water from the pond Trail Camp and filter as I've done on five separate trips now without problems ... if you're really worried, walk around to the inlet on the WNW side of the pond.
I carry 3 liters when I leave Trail Camp for the summit (that is sufficient for me, but some need more). Since I use about a liter for dinner and another liter for breakfast myself, I don't think your plan would work for me. Nor do I personally think it is necessary.
Every hike, I see people who have run out of water on the backside of Whitney. Dehydration contributes to AMS, among other things. It's a real problem.
