Have your teachers written their LOR’s yet? I’m curious how you rate them. My advice on the LOR is that it should highlight the following equation “You” + “UChicago” = “World a better place.” I don’t think you want ones that say “OKCrockets” is a “hard working maths wizz.” I also don’t think you want them to say “OKCrockets” is “one of the best students I’ve ever taught.” The best LOR says something like “I know how UChicago values students who crave learning a subject and here are some examples how I watched “OKCrockets” do that.” Now, you can’t write the LOR for the teacher nor can you review it afterwards. But you can plant that idea in their mind. When my son applied he wrote a thank you note to his LOR writers. First thanking them for taking the extra time to write these and second to tell them that UChicago values the “Life of Mind” and that it would be really helpful if “you could include some examples of me doing that.”
Most of your competition are exceptional students. You need to show how you are an exceptional UChicago Student. You only get one ED1 chance, so you can really make sure your application goes all-out tailor made for UChicago.
I also agree you should do the optional video. It might not hurt you if you don’t, but it will help you if you do and it gives you one more venue to show the AO that you are a UChicago student.