D'Angelo's conjecture for rigid pseudoconvex domains with monomial mixed terms

Let $\mathcal O_n$ be the ring of germs of holomorphic functions at the origin in $\mathbb C^n$, and let $I$ be the ideal generated by $f_1,\dots,f_l\in\mathcal O_n$, where $f_j(0)=0$ for $j=1,\dots,l$. Write

$$m(I)=\dim_{\mathbb C}(\mathcal O_n/I).$$

Let $\Omega\subset\subset\mathbb C^{n+1}$ be a rigid domain whose boundary near the origin is defined by

$$r(z')=2\operatorname{Re} z_{n+1}+\sum_{j=1}^l|f_j(z)|^2,$$

where $z=(z_1,\dots,z_n)$ and $z'=(z_1,\dots,z_{n+1})$. If $m(I)$ is finite, then a subelliptic estimate holds with gain $\epsilon$ satisfying

$$\frac{1}{2m(I)}\leq\epsilon\leq\frac{1}{T(b\Omega,0)}.$$

This is presented as an answer to D'Angelo's conjecture in the special case where the mixed term is a sum of squares of monomials; the cited source does not establish the conjecture in full generality, so its resolution status is unclear.