Kala's ring-theoretic conjecture related to Abhyankar's construction

Let $A=\mathbb{Z}[T_1,\dots,T_n]$, and let $A^+=\mathbb{N}[T_1,\dots,T_n]$. Let $B$ be a subring of $A$ and $I$ an ideal of $B$. Write $QF(B)$ for the quotient field of $B$. Kala's ring-theoretic conjecture. The following situation cannot happen:

$$QF(B)=\mathbb{Q}(T_1,\dots,T_n),\qquad IA=A,$$

there exists $\ell_0\in A^+$ such that for every $a\in A^+$ and $\ell=\ell_0+a\in A$, if $h(\ell)=0$ for some $h(X)\in B[X]$, then $h(X)\in I[X]$, and $\mathbb{Q}\subset B/I$. The conjecture is introduced because the existence of a finitely generated non-additively-idempotent semifield would imply such a ring-theoretic configuration; proving the conjecture would therefore rule out that possibility.