While I understand your frustration the bottom line here is that all the service techs are booked. Which customer should wait while they move your appointment up? The senior citizen without a refrigerator? The family of 6 with no stove? Do you see what I'm saying?

As long as the dishwasher is unplugged, there is no longer a danger of fire. While it is inconvenient to do dishes by hand, it's truly not as bad as being without a refrigerator or stove.