First, a big "Thank you" or "You're welcome" as appropriate to all those who complimented me on how the grass is looking.
I think the biggest part of the improvement is the change is in how the water is being applied. For the past few weeks, rather than water every zone every day, I have been alternating, so every zone didn't get watered every day, but it got a longer soaking when it did get watered.
The quarter-inch of rain we got on Thursday sure didn't hurt, though.
The results have made me optimistic that we can support the entire field on the current water budget. This is still a hot part of the summer, and the grass is coming back. If next year we go into the summer with things green and leafy instead of brown and crunchy, I think that will minimize the time of crunchiness.
Yesterday I went out and changed the sprinkler programming to go even further in the more-seldom-but-deeper direction. Each zone will get a deep watering once a week. The zones on the shade structure side of the LZ will get deeply watered twice a week. If it doesn't do as well on this schedule, I can always change it back.