The Luxury Yacht isn't some game-deciding card. Sometimes it doesn't even get built.
Think of it like a safe consolation prize: If any player doesn't have a better action that is worth 18 or however many points they'd get when they turn their worst ship into a Luxury Yacht (First player doesn't always have the 2-ship!), they can do that, so they have something useful to do at the end.
Especially in 2 player, it seems rare that both players even want the yacht, someone might be trying to get something else done and turned into money before time runs out.
If your problem is just that first player gets first pick of anything, that seems to be a problem with the very concept of firstness, but I don't think it's unbalanced.
Think of it like a safe consolation prize: If any player doesn't have a better action that is worth 18 or however many points they'd get when they turn their worst ship into a Luxury Yacht (First player doesn't always have the 2-ship!), they can do that, so they have something useful to do at the end.
Especially in 2 player, it seems rare that both players even want the yacht, someone might be trying to get something else done and turned into money before time runs out.
If your problem is just that first player gets first pick of anything, that seems to be a problem with the very concept of firstness, but I don't think it's unbalanced.