I cannot answer to what Maxwell knew and what he didn't. What I can tell you is what convinced me that the fields were real and the actions at a distance formulation is wrong. What convinced me was that action at a distance is not consistent with the ideas that momentum and energy are conserved. See, if you accelerate a charge, you can show that it produces electromagnetic waves, draining energy and momentum from that charge. Some of that energy and momentum can later show up in another charge responding to that wave. Without the fields existing as a way to store that energy and momentum, it would just vanish and reappear. With the fields, though, we can keep track of where the energy and momentum are at all times using the Maxwell stress tensor.
Feynman also gives an example of something that is a paradox only if you don't recognize that the electromagnetic field can carry angular momentum. See: The Feynman Lectures on Physics, Vol. II, Section 17-4The Feynman Lectures on Physics, Vol. II, Section 17-4 titled, "A paradox". In it, Feynman describes a situation where turning off a battery driving a solenoid will cause an isolated disk that carries the solenoid to rotate. The paradox is in asking where the angular momentum came from in the absence of any outside torques?
