If I wanted to submit a "all natural cane sugar" (get a golden sugar lump) speedrun, would I be allowed to run multiple instances of the game at the same time? To increase the frequency of the Attempts without altering any RNG? This has been done by the top players in the "just plain lucky" category but I wanted to make sure that it would be allowed i other runs.

I am not sure about rules for a new category(I was unable to find any existing runs)

(a timer and uncut footage from OBS would be availible for verification if nessesary )

Multiple instances are allowed to be running at the same time. As you mention, it's done in several categories, so you'll be fine.

If you're wanting it to become a new category, do everything as usual, then link it in the Discord asking.