Results:
After our first launch but before this second launch, we cut the fins to be smaller which reduced the OpenRocket calculated stability from ~3½ to ~1.9, used a motor with a longer delay so the parachute would eject closer to apogee and not too long before, and mounted the altimeter (for this launch we used a Jolly Logic altimeter two instead of the PerfectFlite Firefly like the first time) in a new 3D printed transition isolated from everything else as opposed to right up against the foam cushioning the egg with no holes cut for the altimeter to get an accurate reading of the air pressure.
Everything mostly went fine, we just need to use a smaller motor next time. We weren't really sure how well it would go with how much worse our first launch did than expected.
OpenRocket simulation file used: SQH rocket 2.ork
