"In essence, my marketing was blaring out “Look, you can share this with your friends!”, without ever actually telling people that the game was worth playing, let alone sharing."

I think this is it, for me. The time I playtested for you was fun, but I didn't really get sucked into the story of the game.

I also didn't consider making my own ship rather than printing or buying. I'm pretty keen to do that now, though! I like craft, and combining that with a game sounds fun. I admit I haven't looked at the shop, but if you don't already, perhaps try selling a "craft kit" version which is blank cards & tokens of the right size and markers?

I also think I care about how much the ship changes - maybe it was just the way I playtested, but I didn't get a real sense that I was changing much, which made me less invested in *my* ship (it could be any ship).

I still love the concept. You're right that the initial player hurdle is big. I suspect once a few people jump that hurdle, you'll get more momentum.