My understanding of the mosquito pattern on Deso/Grey is they are most prevalent after the river drops leaving breeding pools. So the most predictable misery typically occurs after the spring runoff peak as the river is dropping. These bouts only last so long. But obviously you could get a rain induced spike then drop that could encourage a mosquito breakout. All of my Deso trips have either been before the runoff peak or well after and I have yet to experience the reported mosquitos of "biblical proportions" Green River phenomenon.
As for sun, several of my boating friends have found River Sombreros to be a great addition for Deso trips.
River Sombrero - Shade for Rafts!
They can pop them up and down (too much wind? you don't won't to keep even the ones with the strongest fittings up in heavy Deso wind) very easily. Raft passengers tend to love them.