My game, Run Like Dave, also includes an Endless Mode as an optional mode. Players can still choose the 20-second mode if they want a quick session, which aligns with the jam’s requirement for short, 20-second games. The Endless Mode is just an extra option for extended play once the player has mastered the 20-second challenge. I do like your idea of unlocking the endless mode, but unfortunately i ran out of events in Construct to do that and don't want to undo stuff, but if I could I would unlock the mode after collecting a minimum amount of butterflies.
According to the jam FAQ, it’s fine to have other modes longer than 20 seconds as long as the 20-second mode exists as the main experience. So Endless Mode doesn’t appear to conflict with the rules — it just gives players a way to keep having fun after completing the official jam challenge!