<p>My suggestion is to do one of the 4+1 programs such as is available at Haverford or Bryn Mawr: you must major in Physics, CS, or Chemistry, but you CAN double major or minor in anything else. If you have a 3.0 in your STEM major, you move on to a 1-year Master’s in Engineering from Penn. 
And so you get to do everything you wanted without accrobatics and you have a Master’s from an Ivy League school.</p>