Loved it. This type of game are my kryptonite. I didn't end up getting all the endings, so not sure if I was doing something wrong or just needed to restart more times.
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Glad to have made a 'kryptonite'!
Regarding the endings - when you make the final wish, each ending corresponds to each option.
Choose to Stay - Ending #1
Choose to Leave - Ending #2
You'll notice that the third button is greyed out if you take too long. That's because Ending #3 only unlocks if you build the rocket within 10 minutes (timer is shown at the bottom left in white, and turns yellow once you exceed it. A hint is shown when you hover over the button option). Even if you can't beat the timer, each restart permanently stacks rebirth bonuses that each run is guaranteed to be faster than the last.