Typically, black rot is the disease that causes berries to shrivel. (Crown gall is usually associated with graft-unions and trunks and causes vine death.) Removing the mummies from the canopy can help lower the inoculum for the next year, as does vigorous pruning in the winter. More importantly, you'll need to control the disease in the early part of the season with fungicides or canopy management practices.
If you see small, reddish splotches on the leaves (with small black dots in the splotches), that's the start of black rot. The fruit will soon be infected. Once the fruit reaches about 5-10 Brix, it's not susceptible anymore. Most black rot infections occur early in the season (May-June).
If you continue to have problems with black rot and can't control the disease through opening up the canopy or fungicides, you'll have to realize that the site is wrong for that variety or perhaps any variety.