Tree-independence conjecture for biclique-free graphs of bounded induced matching treewidth

For a graph $G$, its induced matching treewidth is the minimum, over tree decompositions, of the maximum size of an induced matching whose edges intersect one bag; its tree-independence number is the minimum, over tree decompositions, of the maximum independence number of a bag. Let $K_{t,t}$ denote the complete bipartite graph with $t$ vertices in each part.

Tree-independence conjecture. For any two integers $k,t\in\mathbb{N}$ there exists an integer $r$ such that every graph with induced matching treewidth at most $k$ and no induced subgraph isomorphic to $K_{t,t}$ has tree-independence number at most $r$.

This would generalize known results relating induced matching treewidth, treewidth, and tree-independence number for classes excluding a fixed biclique. The conjecture remains open.