Chin-Lung Wang's integral Chow-motive conjecture for K-equivalent varieties

Let $X$ and $Y$ be K-equivalent smooth projective complex varieties, meaning that there is a smooth variety $Z$ with proper birational morphisms to $X$ and $Y$ identifying their pulled-back canonical bundles. Let $M(X)$ and $M(Y)$ denote their integral effective Chow motives.

Chin-Lung Wang's conjecture. If $X$ and $Y$ are K-equivalent smooth projective complex varieties, then they have isomorphic integral Chow motives.

This conjecture would strengthen the motivic-integration results in the source from equality in Grothendieck groups, or stable isomorphism after adding a common summand, to an actual isomorphism of integral Chow motives.