Here's the problem with wood in general:
Burl and figure is structurally weak. Straight grain (ugly) is strong. That is why the obsession for the last 400 years has been Walnut. French Walnut, English Walnut, Spanish Walnut, Turkish Walnut, Bastogne, Claro, Black, etc.
And what about that figure? That comes from 1:1000 pieces of walnut where that ugly, straight grain becomes a stunning burl, marbling, or tiger stripe as the trunk becomes the root. A master gun stocker selects for that perfect straight grain at the head and the wrist, then enjoying the option of a burl where it has no structural necessity in the paddle of the stock.
The exotic woods are through-and-through wacky grain structures for the most part. That is not necessarily a good thing.
Then we go to the economics: the labor to shape a stock, inlet, and checker now runs between $4000-$6500 without wood.
Do you want to use an experimental hardwood, or do you want to spend $1000-$2000 on known-commodity walnut considering the intensive labor is the majority of the cost regardless of the wood selected?