We do have a system that people can use to compete for the best times in the Main Levels of Rayman Legends (not the invasions). It's been up for quite a few months. You can find the Google Spreadsheet for all things Main Level ILs here, as well as submission information:

https://docs.google.com/spreadsheets/d/1eTpetdSGwbyQUkFRrEaJ1QAbKG_qPtAcVycVh44p8ls/edit