If you do the following:
1) Enter an unexplored NG+ mine map.
2) Pick up a treasure / open a chest / kill a first-visit-only monster and get an unique drop (not sure if there are such monsters though).
3) Evacuate from the map.
My hypothesis is that you will both have the item, and will be able to enter the map and pick it up again (since "the map returns to its original state").
Can you check it? I don't have any unexplored maps right now.

Chests remain open if they've been collected before (for that game anyway, they're reset on NG+'s)

I believe you can abuse the first time visit only monsters if you really wanted to.

Okay