Still a Slippery Slope....and not a good suggestion.
The solution for the OP's situation is to remove the nest and exclude the wild birds from entering the coop.
Never said it was a good suggestion, just that it was a solution to the parasite insect issue. It does not address other disease issues brought forth by wild birds (newcastles, anyone?)
As a side-note, this is not a slippery slope type issue (At least, not as I have heard the term defined as). Clearly the OP has no issue using permetherin on other pests...