If all the participants to a mix "collect their inputs", then they provide their penalty payment. Then the DOS attack comes in that second step where not all provide their penalty payment. Thus restart and "collect inputs" again. And again, and again and again. Forever.
If the penalty payment is provided before "collect their inputs", then the system knows who is the owner of the input and the output, and thus anonymity is broken.
I don't understand it well enough to give you an answer. *Paging Evan*
I do appreciate that you put time into thinking this through. I might have a read through the debate you linked to when I have some time.