I finally know the culprit behind the Mysterious Day 4 Crash: https://www.youtube.com/watch?v=oh5Dg... The debut of pellet posies that can change color are at fault. Although reds are "discovered" (since their Onion follows me, the Onion produces seeds, and reds appear on the pause menu), the game still hasn't realized that pellet posies that change color can become red if I don't pluck the first red Pikmin.
I suspect that Queen Candypop buds would also crash the game, since they change colors based off of which Pikmin types are "unlocked." However, it doesn't seem likely that we'll be able to encounter one without plucking a red Pikmin first.
Note: it is possible to go to days after day 4 without plucking the red Pikmin (by going to sunset fast and skipping the cutscenes), though the game will still crash on any later day. Additionally, this crash does not "store" between files like Cutscene Timer Storage.
The title is a rip of Stryder7x's videos, go check him out! He does neat stuff with Paper Mario 64.