Strictness of bounds relating the null-additive ideal to the layered ideals E_{I,ε}

Ascertain whether it is consistent that cov(NA) < sup_{(I,ε)} cov(E_{I,ε}), and dually whether it is consistent that non(NA) > min_{(I,ε)} non(E_{I,ε}), where NA denotes the σ-ideal of null-additive subsets of 2^ω.

Background

Using Shelah’s characterization of null-additive sets, the paper shows ZFC bounds comparing the covering and uniformity of the null-additive ideal with the supremum and infimum of the corresponding characteristics of E_{I,ε}.

This question asks whether those ZFC inequalities can be strict in appropriate forcing models, clarifying whether the layered ideals capture exactly or only approximate the behavior of the null-additive ideal with respect to covering and uniformity.