I couldn't let it go. I added two new magnets with better mechanical advantage, and now the flipper stays up.
Now I need to find some screws, model some holes for them, and print the pieces in their final material. I'm thinking matte black PETG on a satin print bed. And keep the magnet inserts in red.
I should probably remove the old magnet from the non-flipping part. It's redundant now.