Yeah your problem sounds different from mine I figured out my mistake which was not picking the ship that required a centurion stripe. I finally figured out that mistake and it worked and updated my quest log. Hopefully someone who shares your problems reads this thread and can offer some help on how to fix the issue if…
I'm stuck on this quest too and tried claiming ships multiple times. What is a regular named ship you claimed? I'm at my wits end trying to get passed this lol.