The following items are not re-obtainable and cannot be stored on the Porter Moogle like other scenario reward items.

Adoulin's Refuge +1
Arciela's Grace +1
Excelsis Ring
Griffon Ring
Ygnas's Resolve +1
Zodiac Ring

I wouldn't bother suggesting adding the NQ versions of the Seekers items, but would like to see the others get this treatment.