Awe, poor baby!
I can agree with giving him showers frequently, but the rest, I just can't...
I would suggest to stop feeding the sweet potato. As per Feeding Feathers Yahoo Group, sweet potatoes may make pluckers pluck more, so removing it from the diet can help.
What pellets is he currently eating? Have you considered Roudybush Rice Diet in case it might be a food allergy?
You mentioned a lot about toys and foraging. Does he actually do any of those activities, or does he ignore his stuff? If he doesn't really play with things, he may need to be taught how.
If you have any pine trees in your area, you might try finding some pinecones, cleaning them the best you can, then heating them in the oven for 20-30 minutes, with the heat on at 200-250° F and use these as an easy foraging/play toy!
Or maybe get some popsicle sticks? Fill a brown paper bag up with plain popcorn, shredded paper, treats, foot toys, etc?
If available to you, find some safe trees that have not been sprayed with any chemicals, cut down a few branches and give them to your grey, leaves and all!
You are right, it's picking, and you've done a great job trying to find out why he's doing it! I honestly don't know, only that you can try and distract him with other things to do and perhaps change around his diet and give more opportunities for play/foraging.