Pewter/Gray on White Oak - Best Option?

I think you could get very close with the fuming ammonia finish. The key to a consistent fumed finish is cutting all the veneer from the same board.
Another finish i like is Rubio monocoat.
Good Luck

-- Aj

I would explore the possibility that this is a multi-step process. It looks to me like the process started with a dark color stain or dye and finished with a a light grey paint wash – or something like that.

I have used a couple that worked well. One was a stain called “Sun Bleached”, but i can’t remember which brand. One was decent one was not the color I wanted. Tried another one that also worked pretty well. I basically bought like 4 or 5 and tested out on the wood I was using.

https://www.homedepot.com/p/1-qt-Oaked-Interior-Weatherwash-Aging-Stain-0091/300664629