Uniqueness conjecture for Schauder-Orlicz decompositions in $\ell_1$ and $c_0$

A Schauder-Orlicz decomposition is a Schauder decomposition whose associated coefficient space is an Orlicz sequence space. Fix the dimensions of its component subspaces. Uniqueness conjecture. Every Schauder-Orlicz decomposition with preassigned dimensions in $\ell_1$ is unique, up to an isometry. Every Schauder-Orlicz decomposition with preassigned dimensions in $c_0$ is unique, up to an isometry.

This proposes uniqueness, up to isometry, for Schauder-Orlicz decompositions in the two classical Banach spaces when the component dimensions are fixed. The source presents both assertions as questions for further study and provides no resolution.