Ultimately, I think they need to alter contribution calculations & I had one other great idea.

Add a quest to unlock ability "Tag Mark", once a Mark is tagged, you & party members who get at least 1 hit in against the Mark are entitled to full-credit.

Call it your due reward for being the finder. Once tagged, the Mark is immune for 2 minutes to provide time for your party to collect. Afterward, the Mark is Tag-immune for another 3 minutes but able to be attacked by anyone.

So you can claim your Marks in this manner. Ineffective against S-Ranks.