She's a large bird, the 1" width may be too small for her?
You mentioned she usually sleeps in the nesting boxes - so she is laying down sleeping that and moving over the 2X4 probably contribute to the worn/broken feathers.
DE is, imho, worthless. It's dirt, very fine and can irritate respiratory systems (yours and theirs). Chickens take dust baths to help decrease external parasite loads, but sometimes they need a little help. Look at your local feed store for a Permethrin based poultry spray or dust. It's safe when you follow directions, it's effective and there is no egg withdrawal.
You can wash her up with soapy water, rinse, dry and use the Neosporin, Vetericyn or Blu Kote.
If she is active, eating/drinking, laying eggs and happy within herself, I would just watch the bare areas for any signs of infection (odor, pus, lethargy, going off feed, etc.)
