I was wondering what everybody else will be using to make their leaderboards, whether you plan to use other external tools, built-in engine features, or even hand-made code. I understand if you guys don't want to share since we're competing. However, I am curious. I plan to use a leaderboard in a future project of mine and was wondering if you had any recommendations.

Personaly I would like to use dreamlo but as I uderstand it will not work on itch.io

You can just make an offline leaderboard according to the rules. Since it needs to be done in a quick and easy way, I would just write a savegame and store it locally. I mean, online would be cooler. I would set something up quickly using Firebase and the REST API.

Was thinking of saving it locally as well.
Maybe if I convert end time into total miliseconds I could save it using Lootlocker leaderboard sorted in ascending order. And convert it back to normal time when showing leader board. Should check that out :)