Can I beat Pizza Tower with Pizzaface Always Chasing me?

What if instead of spawning during Pizza Time, Pizzaface spawned at the very start of each level? Would any of the levels be possible, and if yes, which ones? In this video I've attempted to answer that question, losing a large chunk of my sanity along the way.

In this video, I try to beat every level in Pizza Tower with Pizzaface chasing me the entire time.

Timestamps:

Intro: 0:00
Rules of the Challenge: 1:14

John Gutter: 2:20
Pizzascape: 3:07
Ancient Cheese: 4:49
Bloodsauce Dungeon: 6:02
Oregano Desert: 6:25
Wasteyard: 6:47
Fun Farm: 7:08
Fastfood Saloon: 9:10
Crust Cove: 9:39
Deep Dish 9: 10:11
Golf: 10:44
Gnome Forest: 12:17
Pig City: 15:47
Refrigerator Refrigerador Freezerator: 16:27
OH SH00T!: 17:09
Peppibot Factory: 17:25
Don't Make a Sound: 19:30
Pizzascare: 20:31
WAR: 22:08

EXTRA LEVELS: 25:17
Tutorial: 25:31
The Crumbling Tower of Pizza: 26:00
Tricky Treat: 27:14
Secrets of the World: 27:47

Conclusion: 28:19

Thanks for watching :)