Generalized bounded-critical-number conjecture for $I_{s,t}$-free binary matroids

Let $1\leq s\leq t$. A simple binary matroid is a restriction of a finite binary projective geometry $\operatorname{PG}(n-1,2)$. It is $I_{s,t}$-free if, for every rank-$t$ flat of $\operatorname{PG}(n-1,2)$, its intersection with the matroid is not an $s$-element independent flat. The critical number is $n-k$, where $k$ is the dimension of a largest subgeometry of $\operatorname{PG}(n-1,2)$ disjoint from the matroid. A matroid is triangle-free if it has no triangle restriction.

Generalized bounded-critical-number conjecture. For any $1\leq s\leq t$, the simple $I_{s,t}$-free and triangle-free binary matroids have bounded critical number.

This is presented as a more general problem extending the bounded-critical-number conjecture for $I_s$-free matroids. The source does not state a resolution of this general assertion.