What can I use second chances for in the very endgame?

My main use for second chances was burning them for skills in the actions in the lodgings. However, my character has now reached the level cap in two of them, and I'm growing a hoard of mostly useless Confident Smiles and Hard-Earned lessons.

Is there anything worthwhile I can repeatably cash them in for? With a capped skill they're not very useful for their primary purpose. I know there's that one card in the Nadir, but that's random, and probably won't use the amount of Smiles I accumulate. That leaves handing them out to my acquaintances, but I'd still like to use the ones for skills I haven't capped for myself.