The regular matroid rainbow circuit conjecture

Let $M$ be a simple regular matroid of rank $n-1$, and let $c$ colour $E(M)$ with $n$ colours, each colour class having size at least $2$. Regular matroid rainbow circuit conjecture. $M$ contains a rainbow circuit of size at most

$$\left\lceil\frac{n}{2}\right\rceil.$$

This would extend the known graphic and cographic cases, potentially using Seymour's regular matroid decomposition theorem. The supplied text presents it as a conjectural consequence that remains unproved.