So far, I never used my Whaleship medals for any of those. I get them from daily special maps, daily/weekly/main quests and events instead. So those have a variety of methods to aquire them, but for Whale jewelry, there's only one way. Clearing events and daily quests does take priority over the Whaleship for me though, but I'm also rarely hesitant to spend some FGs to run the whaleship when I don't have the latest jewelry yet. Once the Whaleship missions move to the next phase, the jewelry from the previous phase gets more expensive, so I rather get it before that happens.