That is a beautiful piece! I've owned 3 or 4 Johnny Was shirts over the past ten years, that I bought on eBay - I LOVED them. One was too big, so I eventually gave up and resold it. The other ones I kept for several years, and, you know, you get bored with something, or the color doesn't fit in with the rest of your closet anymore. So I resold them. There is a good market on eBay for secondhand Johnny Was pieces. They're also listed under JWLA and BIYA, if you do an eBay search. I look periodically, to see what people have listed.
The embroidery on the tops I had were mostly done as appliques - embroidery on patches that were sewn onto the shirt, with a little bit of embroidery right on the shirt itself. I didn't ever really have a problem with catching - but I was always very careful wearing the items.
The one thing of note, for their shirts, was that the shirt was cotton, and the embroidered appliques had polyester, so I was always concerned about the shirt shrinking and the embroidery remaining the same size. So I always hand-washed and dried them flat.
For your duster, I see it says "dry-cleaning recommended". I would definitely dry-clean it, and not hand-wash. Just to be safe.