Distinguishing the cardinal characteristics of S_{I,ε} and E_{I,ε}

Determine whether there exists a model of ZFC in which, for some or for all pairs (I, ε) with I a partition of ω into finite nonempty intervals and ε ∈ ℓ^1_+, the covering numbers satisfy cov(E_{I,ε}) ≠ cov(S_{I,ε}), and likewise whether the uniformity numbers satisfy non(E_{I,ε}) ≠ non(S_{I,ε}).

Background

Within ZFC the paper proves certain inequalities and, for many models, equalities between the corresponding additivity and cofinality of the layered ideals S_{I,ε} and E_{I,ε}. However, the relationships between their covering and uniformity characteristics remain subtle.

This question asks for forcing models that separate cov(E_{I,ε}) from cov(S_{I,ε}), and similarly separate non(E_{I,ε}) from non(S_{I,ε}), thereby clarifying the independence landscape for these new ideals.