My mother explained her understanding of the apparent "inequality" to me several years ago:
Adam and Eve are married, and each voices a portion of a covenant they are entering into jointly. Neither is making an individual covenant. There are two parts to the covenant, just as there are two people in the marriage.
Adam voices the part that pledges obedience to God. Eve voices the part in which they agree to work together as partners -- to listen to each other's counsel, and to help each other in their obedience to God.
The split voice helps illustrate that husbands and wives have different but equal roles. Even so, both are bound by the full covenant. Both have a direct connection to God. Neither is an intermediary or an inferior.
The new changes seem to agree with my mother's understanding.
The covenant has not changed, but the revised presentation removes the need to "work around" the awkward split-voice language, and makes explicit the eternal principle that was always there: husbands and wives are equal partners.