Deso is mid-June is unpredictable weather and flow-wise.
June can feel like one of the hottest months in southern Utah as the monsoon hasn't kicked in yet and often get no reprieve from clouds. That said, Deso is its own beast. Expect anything from hot and blue skies to hypothermia inducing 50s and hard, steady rain.
You'll likely be right around the peak but more likely on the taper. If the snow and water saturation keeps up you could experience flows anywhere from the low teens to 40k (2011 peak; this years snowpack exceed that water year). Difficult to predict four months in advance with the odd weather Utah has experienced this La Nina. For comparison, the river peaked on your permit dates at 40k-ish in 2011 and stayed above the mid-30s all of June.
I find Deso most "technical" and challenging the lower it gets. Mid teens is just plain fun. I find it blows out and eases once it gets above the low 20s. That's not to say there aren't consequences but to me the moves get simpler and Deso never seems to be as pushy as its other Green and Colorado brethren at medium to high flows. If its still at or just on the taper from the peak be fully prepared for cold, medium length swims. We could easily see a peak of 40k this year if the March-April snow fall is remotely average. If so, enjoy a fast first couple days.
I would simply recommend your crew be competent at high water Class III and recognize it could be less volume but more challenging as the river drops.
Hope that helps. Great desert float.