How to safely carry sunlight despite high menace?

So, I messed up. My captain has the father’s bones ambition, but I grinded the sunlight trade for echoes long before I had a chance to deliver a mirrocatch box to the fathomking. Now my yearning menace is over 180, and I can’t deliver a box to the fathomking without opening it on the journey.

Is there a way to safely carry a single box for a brief trip without opening it? Or of temporarily lowering my yearning menace just enough to transport one final box? Or am I pretty much screwed here, and have to restart this ambition with a new captain?

I think paying to rest in your lodgings lowers yearning but if I am wrong you can buy a Mountain Sherd in Port Carnelian for 2,000 echoes which will satisfy the Fathomking’s request.

Edit - you can also get a Mountain Sherd in game by making certain choices at Port Carnelian or following a mini quest that starts in Apis Meet.
edited by reveurciel on 1/24/2016

Ah, thanks! I happened to have one on me from fulfilling the embassy quest. A little more expensive than I would have liked, but at least it worked.