Contact Kitchenaid Customer Service.
I know how troubling this little "fire" can be and believe me and the others who have posted, but this could have become a real horror story.
Years ago, my cousin had a KDC18 that had a fire in the dispenser and it not only took out the whole dispenser, but also the racks inside when the plastic melted the lower rack and made a great deal of smoke damage. Luckily, he shut off the breaker right away and had no external damage to his kitchen or the cabinets.
I contacted Kitchenaid at the time and they could not do enough to make it right as they sent a new dispenser as well as a set of racks at no charge.
I could not help get the impression that if I pushed them, they would have replaced the whole machine if I asked them to. But that was not necessary at the time and the machine went on to perform for many more years.
I would not be surprised if you asked them, they may do the same and replace the machine for you. They did that once for me when I had a 23 series tank get a small leak at the heating element that would trip the breaker as soon as the heat came on. As they had a 25 year warranty on the tanks at that time, they wound up replacing the whole machine which I still have and use often. I got a tall tub unit in place of the 23 machine.
I say that you should give it a shot and see where it goes. And whatever you do, do not accept a new machine if they ask for a payment for the exchange. Just tell them that had you not been there, the whole kitchen could have gone up and replacing the machine would be a better deal than having them replace the kitchen or worse, the house.
Since they can't replace the individual parts anymore, what choice would they have?
Nothing ventured, nothing gained.