I understand where you're coming from. My relationship with wool is generally miserable, even the expensive, super-fine, baby merino fancy stuff. And inconsistent: an item that bothers me one day, is fine on another day - so I have a 'three strikes' policy with wool pieces. If it makes me itchy on more than two occasions, out the door it goes. 70% of the time that I wear a wool sweater - even with something underneath - I get itchy on my back, chest/collarbone, and around my hairline.
Cashmere does the same, to a lesser degree. I'd say about 40-50% of the time, cashmere makes me prickly or full-out itch.
I researched cashmere online about a month ago - I have to re-find the article(s), but from what I read, the difference between itchy and non-itchy cashmere has to do with the fiber lengths used in the yarn. As I understand it, higher quality cashmere is less itchy, because the hair is longer, and stays woven into the yarn, instead of unravelling and poking into the skin (and pilling).
I imagine this applies to wool as well.
Loro Piana is supposed to have an excellent reputation for non-itchy, not-as-inclined-to-pill cashmere, but it's far beyond my price range.
I realize this doesn't actually answer your question - but I feel like, if one could track down who a retailer sources their yarn/ knitted fabrics from, it might mean having a reliable supply of non-itchy cashmere?
Overall, I've had the best success with vintage wool and cashmere, usually in the form of fully-lined, vintage coats and jackets. "Seasonless" wool business separates have been okay as well, so long as they are lined.