For all the effort you're making know this: you'll eventually be evaluated by a Gen-X or Millennial hiring manager. We largely don't care where you went to college. We've learned that name recognition means very little. It'll get you a job, but if you're one of those kids who "does nothing" on an extracurricular team, it'll show through on the job. You won't get promoted. We fucking hate micromanaging Ivy League grads who are too scared to take initiative and possibly make mistakes.
Sincerely,
An engineering manager who went to one of the "second-tier" schools you listed.