Conjectural relations among finite multiple-value subspaces

For each weight $w$, let $\mathsf{FMZV}_w$, $\mathsf{FMZV}^{(2)}_w$, $\mathsf{FMSV}_w$, $\mathsf{FES}_w$, $\mathsf{FMTV}_w$, $\mathsf{FMMVe}_w$, $\mathsf{FMMV}_w$, $\mathsf{FMMVo}_w$, and $\mathsf{FMtV}_w$ denote the corresponding weight-$w$ subspaces of finite multiple zeta values, level-two finite multiple zeta values, finite multiple symmetric values, finite Euler sums, finite multiple t-values, finite multiple mixed values with positive last index, finite multiple mixed values, finite multiple mixed values with negative last index, and finite multiple t-values, respectively. Conjectural finite subspace relations. For sufficiently large weights $w\in\mathbb{N}$,

\begin{array}{ccccccccc} \mathsf {FMZV}_w & \subsetneq & \mathsf {FMSV}_w & \subsetneq & \mathsf {FES}_w & \supsetneq & \mathsf {FMTV}_w & \supsetneq & \mathsf {FMZV}_w \\ \text{\raisebox{-2pt}{\begin{turn}{90} $=$ \end{turn}}} & \ & \text{\raisebox{-2pt}{\begin{turn}{90} $\supsetneq$ \end{turn}}} & \ & \text{\raisebox{-2pt}{\begin{turn}{90} $\subsetneq$ \end{turn}}} & \ & \text{\raisebox{-2pt}{\begin{turn}{90} $\supsetneq$ \end{turn}}} & \ & \text{\raisebox{-2pt}{\begin{turn}{90} $\supsetneq$ \end{turn}}} \\ \mathsf {FMZV}^{(2)}_w &=& \mathsf {FMMVe}_w&=&\mathsf {FMMV}_w &=& \mathsf {FMMVo}_w&=& \mathsf {FMtV}_w. \end{array}

The relations are supported numerically except for the middle vertical equality, which is already established in the displayed diagram; the source states that the other relations have no formal proofs yet.