Degree-two regulator conjecture for universal mixed elliptic motives

Let $\ast\in\{1,\vec{1}\}$, let $m\geq 0$ and $r\in\mathbb Z$, and let ${\mathsf{MEM}}_\ast$ be the corresponding category of universal mixed elliptic motives. The real and $\ell$-adic regulator mappings send degree-two motivic extension groups to real Deligne and $\ell$-adic realization cohomology, respectively. Degree-two regulator conjecture. For all $m\geq0$ and $r\in\mathbb Z$, the degree-two real regulator is an isomorphism after tensoring $\operatorname{Ext}^2_{{\mathsf{MEM}}_\ast}({\mathbb Q},S^m{\mathbb H}(r))$ with $\mathbb R$, and, for every prime $\ell$, the degree-two $\ell$-adic regulator is an isomorphism after tensoring the same group with $\mathbb Q_\ell$. This predicts faithful comparison of degree-two motivic extensions with both real and $\ell$-adic realizations; the supplied text gives no resolution.