Using gamejolt’s API, I managed to get online highscores working. To get into the highscores, complete a level, then click on the ‘submit score’ button. You can view the highscores by clicking the ‘community hub’ button in the main menu.
Online highscores currently only work with the standard levels, and I don’t know if I will ever be able to add online highscores for community levels.

Since highscores are simply numerical values, you can’t post spam in them. That’s why I decided to also open up the online highscores to guests. To post custom levels and comment on community levels, you still need to have an account though.
If I notice abuse (like hacking), then the highscores may eventually become member-only in the future to make moderation easier.

Enjoy.

I already submitted a score from each level. While those scores aren’t my best attempts, feel free to show me what some really good times look like ;)