Cuspidal-principality conjecture for the oddball maximal order

Let $\mathcal{O}_{5,!}$ be the oddball maximal order, and let $\operatorname{Vec}(\mathcal{O}_{5,!})$ denote its vector part. A right ideal generated by $x,y\in\operatorname{Vec}(\mathcal{O}_{5,!})$ is called right principal if it has the form $r\mathcal{O}_{5,!}$ for some $r\in\mathcal{O}_{5,!}$. Cuspidal-principality conjecture. If $x,y\in\operatorname{Vec}(\mathcal{O}_{5,!})$ and $x\mathcal{O}_{5,!}+y\mathcal{O}_{5,!}$ is not a right principal ideal, then there exist $r\in\mathcal{O}_{5,!}$ and $S\subset\\{0,1,2,3,4\\}$ with $|S|=4$ such that

$$\\{x,y\\}=\left\{2r, r\left(\sum_{j\in S}i_j\right)\right\}.$$

This claims that the displayed nonprincipal pair is essentially the only obstruction to cuspidal principality for $\mathcal{O}_{5,!}$; the source provides no resolution.