There are many reasons why its not a problem, all delineated precisely in Rav Abadi’s sefer Ohr Yitzchak.
To list just a few…
The mixture of dirty foods, is by itself a totally unappetising combination and can not be considered that the plate “swallowed” a non kosher combination of milk and meat.
Additionally the milk and meat mix together with soap which renders it inedible and so what the plate “swallowed” is technically not even a food mixture.
And there is plenty more to allow it as a first choice.
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