I have also used bird’seye cotton diapers, well washed. These are VERY soft, and can be cut into usable size– about 4″x3″. I don’t use any brush bigger than a very soft camel hair artist’s brush, and I never use a toothpick to clean around prongs in settings. Regular care prevents crud around settings.
Wipe pearls and amber with a soft cloth, and store them in individual velveteen bags. Pieces on display should be in suspension boxes, Riker mounts or secure gem display boxes.
I did carry a large jewelry wardrobe on a trip, and I packed each pearl strand in baby socks!