"It is not, in fact, obvious to the layperson that the Jupiter-Sun System would have a barycenter that doesn't lie inside the mass of the sun."

a point doesn't lie in a mass, it lies in closed surface. ;p

someone, somewhere, might have an 'Aha!' moment from that.

You can't make a physical model of the solar system that has the axis outside the surface of the sun because if the radius of sun and planets was in the correct proportion to the distances of the planets, they would be too tiny to see. Nor would you see the microscopic offset of the axis. If the sun was grossly oversized compared to the orbits (as it usually is), then the tiny offset of the center of rotation would still be visually indistinguishable from being at the center of the sun.

Absolutely, I'm not criticising the construction of solar system models. I'm simply pointing out that if you lack a deeper understanding of the system they represent (or don't interrogate your understanding adequately), the simplifications of any model can quickly become understood as truth.