Is matrix elliptic curve discrete logarithm problem quantum-safe?
Reasoned it through just now. Given the ultimate generator of the elliptic curve group $G'$

Shor $G$ element-wise to obtain an MI $H$ such that $G=H * (G')$, where $*$ is element-wise multiplication.

Shor $P$ element-wise against $(G')$ to obtain an MI $J$

Calculate $J\over H$ using Gaussian elimination to obtain $v$


Yeah! I defeated myself in a cryptanalysis challenge.