You'll find it "written down" in Feynman's autobiographies, he did MIT then Princeton, but that's for physics were there was much more agreement in what physics was. I was informally told the same is true for MIT's chemistry department.
Computer science has not been the subject of thousands of years of study and there's much less agreement on a great deal of it, so there's a higher chance a department will accept its own. But a MIT degree, especially if you do some research, will put you in a good position to get into a very good graduate school. And that should be no problem given what a self-starter the OP is.
"The Advanced Undergraduate Research Opportunities Program, better known as SuperUROP, is designed for MIT juniors and seniors seeking an advanced research experience working closely with a faculty advisor and producing publication-worthy results. Since 2017, the yearlong program has also been open to students in the School of Engineering and the School of Humanities, Arts, & Social Sciences (SHASS)."
Back to getting into a good graduate school, the single best way to get admitted is for a professor at the other school to be told by a professor at your school who he personally knows that you can do research; success in the SuperUROP program would also help demonstrate that, especially if you can get a paper in the process of publication. The other big issue of proving general mastery of the field would be pretty well assumed if you graduated with good marks from MIT.
> Back to getting into a good graduate school, the single best way to get admitted is for a professor at the other school to be told by a professor at your school who he personally knows that you can do research;
that is 100% the correct answer. “hey alice, it’s bob. undergraduate charlie just applied to your department; he’s in my lab now and kicking ass” will trump nearly every other consideration, if alice has funding and tenure.