All runs can be started from a pre-made save file. This will reduce your time spent menuing and you won't have to deal with deleting save files, since each time you start a new game, a new save file is created.

For the Grassy Hub: Disable "Save Automatically". Start a new game, then return to the title screen. You can now start runs by simply loading that file or by hitting continue.

For The Scrapyard: Disable "Save Automatically". Start a new game and then enter the level.
Re-enable "Save Automatically" then return to the title screen.
Disable it once more and leave it off. You can now start runs by simply loading that file or by hitting continue.