See the Grand Enchantment Trail water chart for further perspective on water sources between Beehive Well and Rogers Canyon (Supes).
That's the main water chart, with seasonal updates thru fall 2011. There's also a Google doc version where hikers can contribute more recent observations. See here:
Between the GET info and Fred's chart, both of which include historical observations, you should have a pretty good sense of what to expect in this stretch.
Fred Gaudet's water chart is here:
A few notes:
The "locked" or "permission required" sources between Oracle and Beehive Well are generally along the old route (aka gasline road), while the AZ Trail now follows singletrack trail along a viewful crest of the Black Hills on a somewhat more easterly alignment. I'm not sure whether this route opens up any new potential water sources. Cowhead Well is generally moribund, I believe. (Putnam Spring (good wash flow) is about 3 miles off-route to the east and is reliable, but Beehive Well almost always has some water too, albeit often unappetizing.)
It's been dry lately indeed. However, the winter actually started off with a bang, such that there is certainly some snow lurking yet, even in the southernmost ranges. This may be nearly gone by March without some replenishment, but you'll still have snow on the Grand Canyon north rim, if not elsewhere, if starting at the Mexican border in March this year. Perfect time is impossible, in other words. Actually, though, while the most limiting factor is drought, it's not so much because of the reduced chances of finding water - there's always enough if you're willing to carry - but for the risk of forest closures due to high fire danger. A large-scale closure like the one we saw late last spring, unlike the other factors, is not something you can readily adapt your hike to accommodate. I would guess that your anticipated schedule would get you through to Utah in good stead. Much later, though, and the risk of closures might increase.
Meanwhile, the weather folks are talking about a possible large-scale pattern shift late next week, maybe with greater chances for storms in the Southwest. Stay tuned!