I hate that people use the term “cavendish” instead of actually saying what leaf is involved, so this one may not work for you, but I’ve enjoyed Dunhill’s A-21000. It used to be exclusive to Dunhill stores, but It’s apparently still available in bulk online. (And, yes, still sold under the Dunhill name.) Based on my experience, it didn’t feel like a burley blend, given its lack of nicotine punch. And I enjoyed the flavor a little more than MacBaren’s Vanilla Cream. (But I’m not primarily an aromatic smoker.)
Just be aware that this is a fine shag that burns quickly and needs to be smoked quite slowly, or your tongue will pay the price.