As per the jolly rogers patch, I now have a confirmation from developer that the captains from blackthorn gives you guaranteed 1 ~ 3 Minax Artifacts while shrine contents is live.
Thank you for contacting Ultima Online In-Game Customer Support. We are contacting you regarding your appeal, Ticket#: 9236162. Per the publish notes for Publish 107: "Based on player feedback, all players who qualify for the top contributor list are guaranteed at least 1 and up to 3 minor artifacts per Captain."
Publish 107 – Jolly Roger – Ultima Online This effects both the Fellowship captains as well as the captains in Blackthorn's Dungeon.
So actually, this is a perfect chance for mass gathering Minax Artifacts. The rate of drop is crazy at this moment. I've farmed around 400 points by hunting with buddies one night.