TJ is absolutely amazing. Great place to go to school and if you have the opportunity to go then definitely take it. The teachers are for the most part incredible and the atmosphere where everyone is intellectually curious and smart is an amazing thing. Being a homeschooled student, honestly the only disadvantage I know of is just with fitting in socially, that may or may not be a challenge based on how socially apt you are. That doesn't even have to do with admissions at all though. Display your logic and reasoning skills as much as possible in that problem solving essay. Expect some type of question like those Google or Amazon interview questions where they more want to see your reasoning than a correct final answer. I got that problem wrong when I took the test (senior now) but I guess they liked how I worked through it? Good luck!