Tadić's independence of unitarizability conjecture

Let $\pi_1$ and $E(\pi_1)$ be the corresponding representations constructed in the setting described in the source, where the cuspidal data are transferred from $(\rho_1,\sigma_1)$ to $(\rho_2,\sigma_2)$ with equal parameters $\alpha_{\rho_1,\sigma_1}=\alpha_{\rho_2,\sigma_2}$.

Tadić's independence of unitarizability conjecture.

$$\pi_1\text{ is unitary}\quad\Longleftrightarrow\quad E(\pi_1)\text{ is unitary}.$$

Thus unitarizability is conjectured to be independent of the choice of the corresponding cuspidal data. The supplied text gives no general proof or disproof.