Twisted diagonal deformation conjecture for maximal representations

Let $G$ be a Lie group of Hermitian type, and let $\rho:\pi_1(\Sigma)\to G$ be a maximal representation. A twisted diagonal representation is a representation obtained from the diagonal embedding of a finite cover of $\mathrm{PSL}(2,\mathbf{R})$ into $G$, together with a twist by the compact centralizer of its image.

Twisted diagonal deformation conjecture. If $G$ is not locally isomorphic to $\mathrm{Sp}(2n,\mathbf{R})$, then every maximal representation

$$\rho:\pi_1(\Sigma)\to G$$

can be deformed to a twisted diagonal representation.

This conjecture predicts that, outside the symplectic case, all maximal representations lie in deformation classes containing twisted diagonal representations. The source gives no evidence of a resolution.