Is there any way to reset the progress to start a new game, without having to complete all 4 areas?

I'm not sure myself but you may have to delete the steam cloud save.

I just finish every run I do. It's tedious as hell and probably not the only way. Hopefully there's a future patch to reset progress in the options. Do not just start back at area 01 though. Runs must be done from reset progress.

Although finishing out every run has helped me learn some new movement and helped me get more consistent on other levels, so it's not all bad.

Well, I have found that the game stores its save in C:\Users\¤username¤\AppData\Local\You_Have_10_Secondsfinal, as a file named game.ini. Deleting that file will reset the saves. Will this be allowed for runs? I don't see why not..

As long as you're starting from a fresh save it should be fine.

Yes, that's fine. It's up to you. I believe I tried deleting that file once but then I couldn't launch the game. I then had to reinstall through Steam. If you can get it to work, go for it.