Summerset Vault of Moawita: Can I reset and restart the quest?

Ulfson

Several months ago I abandoned the quest Vault of Moawita given in College of Psijics Ruins. And I suspect that I deleted several museum pieces from my inventory. I went back to the quest giver in the college and can't get the quest again. One piece is in a museum case from months ago. I have The Psijic Codex. But several of the chests are not appearing for me to loot.
Does anyone know if or how I can reset the quest and start over?

Happy Trails