Thank goodness I was not hosting dinner at my house.
I have pulled out the trusty allen wrenches to see if I could do any further damage from outside the disposal unit. Nope. None of the wrenches fit into a solid footing from under the unit. I'll be back to broomsticks and tugging on the cloth tomorrow. Tonight I'm turning off the lights in the kitchen and turning on a movie. Yep, run away...my favorite method for tackling problems beyond my scope.
Update tomorrow :D