Finished 約束, the booklet that came with the drama CDs. I can confirm that there doesn’t appear to be anything CD-specific about it, so we’re good to keep including these in our bonus reading. 
Timeline-wise this slots nicely right after book 3 (and presumably drama CD 3), and features three different POVs: Kaito, Geoffrey, and Vicente.
Kaito takes a bath onboard the Gloria; he mentions Nigel fulfilling a promise to him in regards to it, but it’s been long enough since volume 3 that I don’t remember the specifics. 
Geoffrey, interested in the prospect of seeing Kaito naked, makes a pest of himself until Kaito calls Nigel over to chase him away. Interestingly, it seems Nigel’s already been making efforts to chase away other peeping Toms; this story makes some small callbacks to ミニアと呼ばれた男, specifically Nigel’s seasickness and, more relevant to this story, desperate sailors having sex with farm animals.
We’re already getting hints here of Nigel’s feelings for Kaito, far earlier than in the main books. Geoffrey picks up on it pretty quickly as well, though I’m not sure if he’s guessing correctly at the depths of those feelings.
Surprisingly, we also get a quick change of scenery to Vicente and Leo; Vicente’s apparently come down with a fever from the wounds he sustained with his fight against Nigel, and Leo’s taking care of him. I was a bit surprised to see him him, but it makes sense; there’s a pretty long interval in the main books from his appearance in volume 3 to his next mention, so it’s good to check up on him after the fight.
Overall a nice little story; it felt like a cut chapter from the main books, honestly. I could see this being set between big moments: there’s good camaraderie and ship-building here, but nothing necessarily significant in terms of plot.