I also have a character that ran into this about a year ago. I ended up just getting the green one as my third operative but it would be great to see a fix.
Yeah I have tried switching in space as well as renaming to make sure it wasn't something to do with the name. I contacted support and the answer I got was unknown bug submit a bug report and post to forms.
This is what the ship list looks like. Strangely enough the offending ship has the ready starship button active although clicking it does nothing. As for the point about having a shuttle active, I did try commissioning a shuttle to see if that might fix things but that just resulted in having all three active.