Since all the stages in the main game take the same time to complete, the full game speedrun becomes about mashing and driving the bus faster for around 2 hours, until you can finally reach the final level: The Peckening, which is actually the only stage in the game where being faster actually matters.

My suggestion: Do just like the google sheet Leaderboard and use score-based speedruns for all the common levels, and let The Peckening be the only time-based speedrun level. This would let more people get into speedrunning Overcooked (and Overcooked 2, which will be released quite soon), as they would have to worry only about submitting the scores, and not having to do a lot of the hassles that come with using livesplit and such. The google sheets Leaderboard currently uses that format and has quite a few people submitting scores to it.

Link to the google sheet Leaderboard: (https://docs.google.com/spreadsheets/d/1DQEGWjW4_T6Swlsdxe0yKhXpRyTJQ29LZqrJjI5CeWY/edit?pageId=104841529160870569487#gid=0)

High scores obviously work better for this game. As I see it, there is no way to do that on Speedrun.com so you can post all high scores on the google spreadsheet.