Been a few times on Memorial Day weekend. Water was pretty predictable, but now they close the highway for the bike race, which would complicate logistics, and it's still pretty cool weather then. Went once in July; got a hot day, big rise in the level for the second day, and lots of "action" in the gorge. Memorable, if you catch my drift. Have tried to time things for a sane level after the peak, but seems like when it drops out, it REALLY drops out. Much less of a problem if you're local, but being a long day's drive away makes that tougher.
Maybe a week or so after Memorial Day - after the bike race, before the usual peak. Your results may vary (like 2-3 years ago, when big snowpack heated up early. I think the peak hit 8500-ish in latter part of May.)
It's a dandy overnighter, though. Get someone to hustle your food and camping gear on the train, then run your shuttle. Very nice way to go!