These weren't hard to make as you just built out from the start and added random branches, or dead ended them occasionally.

It's expensive, but the taste isn't really distinctive (unlike their truffle gin, which is very unusual).

Next, instead of pre-seeding the ship with keys, you have it generate them (using its RTG for both power and a source of entropy) and send them back to earth at a fixed rate, possibly with the size of the keys increasing over time.

On earth, when you want to encrypt a payload to be decrypted at a future date, you calculate how many round trips it would require, then encrypt the data with that many keys from the stream, interleaved with keys generated locally. As the time will unlikely be an exact round trip time (which is ever-increasing), each end can delay the decrypt and re-transmission for some proportion of the remaining time.

I also feel like songs I replay in my head (which I do constantly, and without a choice in the song) have very high fidelity.

I don't think believing makes you gullible, is just that the consequences for believing in this case are negligible. At worst, you repeat the story to someone else, as second-hand fact. Mostly likely however, you'd never think of this conversation again, and it would have no effect on your behaviour. I think it says much more about the person telling the lie (this is a shitty thing to do to a friend) than the person accepting the lies.

Extraordinary claims may require extraordinary evidence, but it really only matters at the point where believing those claims affects one's behaviour and the consequences are tangible and different from refutation of those claims.