Almost Cohen–Macaulayness conjecture for Rees algebras of monomial almost complete intersections

Let $I$ be a monomial ideal of $k[x_1,\ldots,x_n]$ that is an almost complete intersection of finite colength, and let $\mathbf R=k[x_1,\ldots,x_n]$. Its Rees algebra is $\mathbf R[I\mathbf T]$. Monomial Rees-algebra conjecture. The Rees algebra

$$\mathbf R[I\mathbf T]$$

is almost Cohen–Macaulay. This concerns the homological behavior of Rees algebras for finite-colength monomial almost complete intersections; the source gives the assertion as a conjecture and supplies no resolution evidence.