Here are the solutions I found for the sodoku puzzle and the best RNG for the crossword:

https://imgur.com/a/qcsVc61

I was hunting down all of these too until I found a skip for the laser security which skips the sodoku puzzle. This will be useful for people that don't want to do the skip.

Would love to know more about that skip. Tried to find a video of it and couldn't.

https://twitter.com/i/status/1352422153581334530

I ended up messing around myself as well yesterday and figuring it out too. My method looks the same from what I can tell. Figured I would post mine here too for more science/research. This was on the PAL version, running the game on the most up to date version of Duck Station.

https://www.twitch.tv/kefka14/clip/AbrasiveBashfulClamVoteYea-NMaYm9MsZLroJrFS