I have read all of your posts to date. I think you are seriously underestimating how much water you should carry.
June is the hottest, driest month in Arizona. I am planning a trip in the Canyon in early May, which is a lot cooler than June, and I will never start the day with less than 3 liters in my pack. I probably won't need all of it but it is there if I do. I would carry at least a gallon if I were going in June. Temperatures in the canyon in June can easily top 100 degrees and the relative humidity can be as low as 5%; this combined with strenuous hiking can be a deadly combination.
Yes, there are water sources along the Bright Angel trail and at the river and at Cottonwood. But, especially going uphill with a pack, you can easily sweat away a couple of liters per hour and you won't really be aware of it; the sweat evaporates as it is produced. What can happen, and does frequently happen, is a progressive dehydration leading to unusual fatigue and that can also affect ones judgment; a hiker should stop and rest in the shade but keeps on plugging instead. The best outcome under these circumstances is to finish a trip with a splitting headache and super sore muscles; the worst thing that can happen is that you can die. It happens to canyon hikers every summer! And, most of the rescues, and fatalities, are along the corridor trails you are proposing to hike and mostly involve fit, young people.
Carrying six to eight pounds of water to start the day is a small price to pay for a safe and enjoyable trip. I urge you to rethink your water needs.
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