Finite-order separation conjecture for Cantor series

Let $t\geq2$ be an integer and suppose that $\{1,\ldots,t\}=A\mathbin{\dot\cup}B$. Let $Q$ be a basic sequence, and say that it is $t$-divergent when the relevant divergence condition holds through order $t$. Finite-order separation conjecture. There exist a real number $x$ and a $t$-divergent basic sequence $Q$ such that

$$x\in\bigcap_{k\in A}\mathscr{N}_k(Q)\backslash\bigcap_{j\in B}\mathscr{N}_j(Q).$$

This asserts that, for a suitably chosen $t$-divergent basic sequence, the normality orders in $A$ can occur while those in $B$ fail. The source says the conjecture is almost surely true and that the preceding nonlinear-system conjecture would imply it, but no proof is supplied.