Update 7 is here and it includes a Speedrun Mode!
You can toggle it on or off by hitting the F1 key at any point in the game.
It's pretty lightweight. All it does is drops a clock on the top left hand corner of the screen that tracks your run time and shows your stats.
It also enables a few hotkeys. You can use Tab or Shift+Tab to scroll between levels and hold the Restart key to restart your run from the beginning.
My record is 2:06.
But that's only because I can't type the cheats to skip levels any faster.
I think I can manage a minute fifty if I put some more effort into it.
Cheers