Alright, here's what I found through replaying.
If you go through it from day 23 to day 25 all at once without closing out the app, it seems to work fine (as long as the stat-exchange doesn't come back).
I have a hypothesis that the reason it doesn't work if you close it out is because the secondary screen that opens up for the rod is saved in the background or something and the multiple screens break the game.