Hamidoune's bounded symmetric-exchange conjecture

Let $M$ be a matroid of rank $r$, and let $(A,B)$ and $(A',B')$ be compatible basis pairs, meaning that

$$A\cap B=A'\cap B'\qquad\text{and}\qquad A\cup B=A'\cup B'.$$

A symmetric exchange is an exchange of elements between the two bases that leaves both resulting sets as bases. Hamidoune's conjecture. For any compatible basis pairs $(A,B)$ and $(A',B')$ in a rank-$r$ matroid, the first pair can be transformed into the second using at most $r$ symmetric exchanges. This optimization variant unifies the disjoint-bases transformation proposed by Gabow with White's compatibility question; the source gives no resolution, so the conjecture remains open.