I still don't get why you want to work at a HF at all. You say you want to apply your quantitative skillset, along with the increasing prevalence of algo trading and the job security. Are there not other streams where you can apply your particular skillset? Do you think you'd enjoy a specific role at a HF? Do you want it because it seems lucrative? Are you interested in mathematics and/or CS?
"I was looking at MFE programs because I've heard that they're required for any role that is quantitative." That seems false to me, but I can't give a definitive statement on something I don't know. Yes, self-teaching can apply to many, if not all programs. Coming from a strong program sure would help, but it isn't a necessity. My intuition tells me that if I'm a kid from a subpar school who has the knowledge, taken multiple advanced graduate courses, done PhD-level research, all in his second year at undergraduate, a lot of the top firms would be willing to give me an interview for an 'xyz' job relating to mathematics. Note that I don't know much about HFs, I simply want the point to get across. Of course, weigh out what matters in your life. If you believe in your capabilities, you can achieve a lot in the vicinity of your own home, provided you have little to no desire in engaging in other activities. I should add, it'll provide you with much more than the skillset to be a competent employee.