Weak knitwork immersion conjecture for bounded-treewidth classes

Let $k,d,\ell\geq 1$, let $\Delta\in 2\mathbb{N}$, and let $\Omega=(V(\Omega),\preceq)$ be a well-quasi-order. Let $\mathbf{T}(k,d,\Delta,\ell;\Omega)$ denote the class of $\Omega$-knitworks defined in the paper, with the indicated parameters. Let $\Omega$-knitwork immersion be the immersion relation on these objects that respects the quasi-order $\Omega$.

Weak knitwork immersion conjecture. The class $\mathbf{T}(k,d,\Delta,\ell;\Omega)$ is well-quasi-ordered by $\Omega$-knitwork immersion.

This conjecture removes the strongness requirement from the corresponding negative result for one unbounded-degree vertex and is intended as a positive complement to that obstruction. The supplied text gives no resolution.