Uniformity conjecture for Galois-conjugate hyperbolic representations

Let $M$ be a hyperbolic 3-manifold and let $\rho:G\to \operatorname{SL}(2,\mathbb C)$ be a lift of the discrete faithful representation associated to its hyperbolic structure. Suppose that $\rho$ has entries in $\operatorname{SL}(2,K)$ for a number field $K$ with a real Galois embedding $\sigma:K\to K^\sigma\subset\mathbb R$. Let $\rho^\sigma:G\to\operatorname{SL}(2,K^\sigma)\subset\operatorname{SL}(2,\mathbb R)$ be the associated representation, and suppose $e_{\rho^\sigma}=0$ in $H^2(M;\mathbb Z)$. Let $r$ be the relevant rotation quasimorphism on the universal cover and write $\phi=r\circ\widetilde\rho^\sigma$. The uniformity conjecture. The quasimorphism $\phi$ is uniform. This would produce uniform structures from real Galois conjugates of the hyperbolic representation, but the source gives no resolution of the assertion.