I decided to make a sub-category for each stage in this category. One subcategory for each level. This because running the full thing is a marathon. I don't know how long it would take but it will be brutal, good luck to anyone wanting to run all 350 puzzles + 7 bosses with no skips or hints. The subcategories were made to bring all the puzzles into play.
If you want to run any of the subcategories from level 2 to 7 you MUST use the "CHISLER" cheat to skip any prior stage. Say you want to run the Coyote level without having to complete earlier stages. You just make a new game, then hold "Alt" while typing "chisler". A window will pop up where you can change the level to 4. Once you have done this you can click on New York City (which should still be on the map), but after entering it it will tell you you completed this level. When you get back out on the world map the cities from the level you set should be there. Your run starts when you enter any of these cities and finishes once you hit "continue" after clearing the boss stage. Note that if you enter any level prior to starting your run then your speedrun will be DISQUALIFIED. This is because you can make the game skip the "tutorial" for each type of puzzle if you've entered it prior to starting your run, thus saving time. This is important to streamline runs.
You can see how i set up the run in the beginning of this video:
Please make sure your video capture software captures the pop-up dialogues making the run easier to verify.