Given that a spacecraft's purpose is to leave the Solar System as fast as possible, how deep into Jupiter's gravity well would be optimal for an assist in the planet's orbital direction? Jupiter's max orbital speed of 13.7 km/s sets an absolute upper limit for gravity assist, but by how much could the Oberth effect contribute?
Juno now gets to 4,200 km of the cloud tops (by some definition of cloud tops). Would it help much for a high speed spacecraft getting down to 0 km and fire the last instantaneous propulsion stage right there? Aerogravity assist would only help change the inclination, not improve the maximum Solar System escape speed, is that right?