Having known most of the AMD 9W agents - I am pretty sure that they wd not consider the DL Elite status and go only by the rule book - allowing you 2 bags! Having said that, if you can get Delta to respond in a mail (or something in written), few far stretched chances - Though high probability that even that won't be accepted - 9W would just go by the rulebook!
However worth taking a chance by asking someone to wait in the hall way till the checkin is complete - If it goes - it goes and it they ask additional baggage fees, safe to return it to the waiting family member
