Have you tested your soil?
proper Ph for zukes is 6.0 to 7.5
Look for "fraz" around the base of the vines, if you find that, you do have SVB's..

Watering overhead, rainy spells, and over watering can, and will "clump" your pollen, However, you say that the blossoms don't open enough to hand pollinate, so I would think that in itself would shelter the pollen, thus protecting it from the water/rain