Representable $*$-regular rings and ultraproducts of artinian rings

Let $R$ be a $*$-regular ring. It is representable if there are a vector space $V_D$, a ring embedding

$$\iota:R\longrightarrow \operatorname{End}(V_D),$$

a $*$-hermitian form $\Phi$ on $V_D$, and the property that $\iota(r^*)$ is the adjoint of $\iota(r)$ for every $r\in R$. A ring is subdirectly irreducible if it has a least nonzero congruence. An ultraproduct is formed from a family of rings with respect to an ultrafilter.

Representable-ring ultraproduct conjecture. Every subdirectly irreducible representable $*$-regular ring can be embedded into a homomorphic image of a regular $*$-subring of an ultraproduct of artinian $*$-regular rings.

The conjecture would connect geometric representability with constructions from artinian $*$-regular rings. The source presents it as open and separately asks whether every $*$-regular ring is representable.