I have a butternut shelf screwed between the legs of a table with pocket
screws. Since that is not particularly secure, I put a support under it,
also between the legs. To avoid problems with wood movement, I made the
grain run the same as the shelf; actually I just used cutoffs from trimming
the shelf. So, while it is better, it still isn't too great.

I had a brilliant idea; replace the butternut support with a walnut support
with grain running the other direction (across the shelf). Because of the
improved grain direction and the improved material, it will be many times
stronger.
I figure I can do this because, according to my chart, walnut moves
grainwise almost as much as butternut does cross grain. And if anyone
notices the different wood, it will simply look like a design accent.

Is this idea sound?

You probably wonder how I ever get anything built, working like this.
Fortunately I have a lot of time.