The Strong Diamond Conjecture for full loci of covers

Let $((X, \omega), \mathcal{M}, C_1, C_2)$ form a generic diamond, where $\mathcal{M}_{C_1}$ and $\mathcal{M}_{C_2}$ are full loci of covers with covering maps $f_i$. Assume that, for $i=1,2$, the closure of the cylinder locus in $C_{i+1}$ satisfies

$$\overline{\operatorname{Col}_{C_i}(C_{i+1})}=f_i^{-1}\left(f_i\left(\overline{\operatorname{Col}_{C_i}(C_{i+1})}\right)\right).$$

The Strong Diamond Conjecture. Under these assumptions, $\mathcal{M}$ is a full locus of covers. This would extend the full-locus conclusion beyond the cases established by the preceding results; the supplied text does not state whether the conjecture is open or resolved.