Wolf: I may be mistaken, but i believe that the din of Chalal only applies to issurim specific to Kohanim (e.g. gerusha), as opposed to issurim that apply to the rest the Kahal (mamzer). So if a Cohen would have mamzer offspring his children would not be Chalalim. This is my understanding of the sugya in Kidushin daf 77b.
In addition, I don’t understand your statement that a the child of a forbidden kohen marriage loses Kohanic status. It is my understanding that they are a Kohen Chalal which means they lose the benifits of being a Kohen, but not that they aren’t a Kohen altogether. Please tell me if I am mistaken.