I haven't successfully been able to overcome this because I'm not sure if there is a trigger for a 'countdown' for the fella to spawn before I have everything. Because of this I haven't confirmed what I expect to be the solution. I've had an early spawn of a suspected specific item with no intentional action/choice prompts, and then absolutely nothing while spamming all activities that may trigger rng spawns. I might be barking up the wrong tree and it's part of a different ending, but it's one of the possible artworks we receive in a bottle with roman numerals. Fred and Row also have dialogue that drop hints on the possible solution. The smallest part I have received from a crewmate just having it. Pushing through their dialogue options persistently as the days go by (1-2 chats/day) sometimes seems to help. I've also fished it up. Chests may also contain a part. The only guarantee part is during red time. Have a bucket for medium, and net for large.
I got very close to rescue once, but the most unfortunate of happenings meant I lost any mayday items during the rescue operation. I also am not sure if D's hat triggers something, or increases the likelihood of something. The narrative in my head is that the hat leads to mistaken identity, which may aggravate. I'd love to hear any of your own theories/experiences as well. I want to crack the code organically, as the mystery of the systems and the story itself is all part of the fun!