I know your pain. I have been using dishwashers for a tad over ten years and the worse thing that can happen is dish soap getting into one. I have four sons in this mans home and I can assure you our sons have placed dish soap into it a few times, you know helping the rents clean. OOPS and its suds city and kids giggling. Wife and I can only watch this unfold and laugh.
I think at one point we put large bowls inside of it to trap as much of them as possible empty them in the sink and continue the cycle. But we just kept running it almost empty a few times and hand washed the dishes few times. It reduced over time. and there was no damage done just a lot of mopping a giggling children.