Jhine....Your link points out the Hebrew idiom "dying you/they shall die" was often used in the OT. Never in those usages does the expression suggest "eventually" or "gradually" as the writer of the article proposes for Genesis 2. Yes, the "the day" was referring to the day they ate, but it equally refers to the time of death. Elsewise the inclusion of "the day" becomes superfluous.
It is difficult to extrapolate exactly what (J) had in mind but likely his brief narrative was meant to stand alone as a warning tale. The expansions and bridges of later redactors created the continuity issue. Possibly the redactor and later sages were not concerned by this as they had inherited a larger body of tradition that made some explanation possible even obvious. (i.e. God's mercy.)