My use of chemical treatment is just something I am used to. My experience in Zion has been that water is plentiful, good and flowing. Many canyons on the west side of Escalante also have water. You probably would not have to deal with seeps, but rather with flowing water or at worst some standing pools.
Water carrying requirements obviously depend on your consumption. For me carrying more than 4 liters is not practical (too heavy). Of course it depends on the outside temperatures, but normally I assume that 4 liters covers my needs for one day (and some).
If you need more information on the routes, then Michael Kelsey's non-technical canyoneering book and Steve Allen's Canyoneering 3 are great sources. For Zion, Tom Jones' guide is standard. On the Internet I would check http://climb-utah.com/, "Average Joe Road Trips" and "Todd's Desert Hiking Guide". For questions on the current conditions check forums on http://bogley.com/ and http://canyoncollective.com, you can ask for current info there.
If you somehow can fit it on the way between Zion and Escalante, Buckskin Gulch is a great destination. It would give a taste of a slot canyon. If you are fast, you can hike down Buckskin and up Paraia in a day easily. Or camp at the confluence. Do check conditions for a possibility of mud or mandatory swims. It is likely dry however. Be very mindful of thunderstorms (flash flooding).
In Escalante area (although not normally backpacks) the flowing creeks like Calf Creek, Boulder Creek, Deer Creek are all awesome hikes. The more water, the better the route. If nothing else, just hike to lower Calf Creek falls from bottom and top on the last day.
Looking at your gear list, you seem to be really minimalistic. So, perhaps a light silnylon 35L dry bag might work well. If it does not last long, no big deal.
If the forecast is completely dry, you could leave rain gear at the trailhead. Coyote Gulch has some massive alcoves and overhangs in the upper part (like 100 yards deep) and some small overhangs lower. Potentially you could just use a bivvy.
In the late May or June (depending on the year) high and open areas in Utah start getting tiny gnats (Escalante). Any wind or any movement will eliminate them. They are not active at night. But if you are parked and no wind and gnats are swarming, it's really hard. Long sleeves and a small head net will make a huge difference. DEET does not work.