Purity conjecture for tensor products of almost strictly pure t-modules

Let $\phi$ and $\psi$ be two almost strictly pure $t$-modules over $K$, and let $\phi\otimes\psi$ denote their tensor product. Choose a $K\{\tau\}$-basis of the corresponding $t$-motive. Purity conjecture. The tensor product $\phi\otimes\psi$ is almost strictly pure if the basis is chosen appropriately. This asks whether the near-purity observed for tensor products of rank-$2$ Drinfeld modules extends to tensor products of arbitrary almost strictly pure $t$-modules; the statement remains open in the supplied text.