I think your drawstring analogy is probably a more accurate way of describing what should happen. Think of the size of the oval, as the difference between a pencil and a windstick.
As for your second question: At some point you need to experiment with tongue arch. Letting the tongue float up in the oral cavity in the “ee” position. I would also recommend thinking about releasing the airstream in an upward direction. This helps to keep the aperture open and not to collapse into a pinch. Good Luck!