I thought this was a really cool idea! If you don't want to go to an online leaderboard, maybe just having certain times relate to trophies could work? It would be fun if you were competing towards some specific goal or trying to finish the level before you timed out.
For the sake of the jam I avoided anything like that since I feel that would have been quite the steep learning curve.
I will definitely will look into the online scoreboard. It was something i briefly considered but then left the idea out. I do like the concept of being able to see how other people did. I imagine that the online scoreboard would give people a nice incentive and goal to focus on rather than trying to better their own local score.
As for timing out. Some of the puzzles that will be coming in with the update can take a little while to solve and didn't want to really punish anyone for taking a bit longer to complete a level.
But that could possibly be added in as a challenge mode to really push people. Thank you for the feedback. It has me thinking about a few additions that can be made now.