We use Skin-So-Soft by Avon for everything! It gets out tar, sap, grease, etc., plus keeps bugs away! Have used it on other animals without incident...don't know why a chicken would be any different.
Thanks for the wonderful ideas! Definitely have Dawn dish soap and Avon SSS both on hand. I'll try one of those in the morning- for now, she's sleeping quietly with a full belly.
As for the hair cut- I like the mohawk idea. I just need some clarification. When I clip the feathers (I'll probably use dog nail trimmers like you suggested- less likely to poke an eye out), do I clip all the way down to her head, or part way down the feather shaft. I'm relying on you Polish loving folks! I have another polish hen (a silver laced) that doesn't have this problem (yet)- her crest has stayed nice and poofy on the top of her head, where my BW hen's flops all over.