What was Feynman's "much better way of presenting the electrodynamics" -- which did **not** appear in the Feynman lectures? Does anyone know what Feynman was referring to in this interview which appears at the beginning of The Feynman Tips on Physics?  Note that he is referring to something that did not appear in the Feynman lectures.

I didn't like to do the second year, because I didn't think I had
  great ideas about how to present the second year.  I felt that I
  didn't have a good idea on how to do lectures on electrodynamics. 
  But, you see, in these challenges that had existed before about
  lectures, they had challenged me to explain relativity, challenged me
  to explain quantum mechanics, challenged me to explain the relation of
  mathematics to physics, the conservation of energy.  I answered every
  challenge.  But there was one challenge which nobody asked, which I
  had set myself, because I didn't know how to do it.  I've never
  succeeded yet.  Now I think I know how to do it.  I haven't done it,
  but I'll do it someday.  And that is this: How would you explain
  Maxwell's equations?  How would you explain the laws of electricity
  and magnetism to a layman, almost a layman, a very intelligent person,
  in an hour lecture?  How do you do it?  I've never solved it.  Okay,
  so give me two hours of lecture.  But it should be done in an hour of
  lecture, somehow -- or two hours.
Anyhow I've now cooked up a much better way of presenting the electrodynamics, a much more original and much more powerful way than
  is in the book.  But at that time I had no new way, and I complained
  that I had nothing extra to contribute for myself.  But they said, "Do
  it anyway," and they talked me into it, so I did.

Did this approach to teaching electrodynamics appear in any of his later writing?
 A: I am not sure, but maybe this is about Feynman's derivation of the Maxwell equations outlined in Dyson's article http://signallake.com/innovation/DysonMaxwell041989.pdf (Am. J. Phys. 58(3), March 1990, p. 209). However, my impression was that derivation is deficient.
A: I spent a long time researching this question for Carver Mead (mentioned by Art Brown) in 2008, because we were both curious what Feynman meant. Carver thought Feynman's "better way of presenting electrodynamics" would be something along the lines of his own "Collective Electrodynamics," but that turned out to be only partly true, as I discovered in four pages of Feynman's notes, written during the year he was teaching the FLP lectures on electrodynamics, which briefly explains his new program. [These notes can be found in The Caltech Archives: Box 62, Folder 8 of The Feynman Papers, "Working Notes And Calculations: Alternate Way to Handle Electrodynamics, 13 Dec 1963."] I asked Matt Sands if he knew anything about it, and he told me that in about the middle of the 2nd year of the FLP lectures, Feynman started to complain that he was disappointed that he had been unable to be more original.  He explained that he thought he had now found the "right way to do it" -- unfortunately too late. He said that he would start with the vector and scalar potentials,  then everything would be much simpler and more transparent. The notes are much more detailed than that. Unfortunately I don't have the right to publish them myself (without asking Caltech's permission)... but there is a plan to digitize the Feynman Papers and put them online - funding is being sought for that now.
Mike Gottlieb:
Editor, The Feynman Lectures on Physics & 
Co-author, Feynman's Tips on Physics
P.S. As mentioned in my comment below, the notes have been posted. They can now be found here.
A: Opening with an aside:
Interestingly, one of Feynman's students, Carver Mead, of VLSI fame, expressed similar dissatisfaction with these EM lectures and actually wrote a monograph, "Collective Electrodynamics", which attempts to reformulate the discipline using the potentials, not the fields, as the primary entities, and quantum systems (superconducting loop, coherent quantum resonator) as the canonical examples.  
It's not a difficult read.  I'm not qualified to pass judgment on its success, but I do know I wouldn't want this approach to be my first course in EM.

Anyway, all that is only tangential to your question.  I believe the interview you quoted is from 1966.  Much later, in 1983, Feynman gave a series of public lectures on his theory of Quantum Electrodynamics (QED), which were subsequently published as QED, The Strange Theory of Light and Matter.  
The bulk of this book describes the probability amplitudes of interactions of photons and electrons, and their applications in various settings ("calculating the sum of all the little arrows").  Near the end of Chapter 3, there is a schematic argument which may refer to the "1966 approach":

There are circumstances, for example, where the amplitude to emit a photon by a source is independent of whether another photon has been emitted.  This can happen ... when a very large number of electrons are all moving the same way, such as up and down in the antenna of a broadcasting station or going around in the coils of an electromagnet.  Under such circumstances a large number of photons are emitted, all of exactly the same kind.  The amplitude of an electron to absorb a photon in such an environment is independent of whether it or any other electron has absorbed other photons before.  Therefore its entire behavior can be given by just this amplitude for an electron to absorb a photon, which is a number - called a "field" - that depends only on the electron's position in space and time.... When we take polarization into account, there are more components to the field.  (There are four components - corresponding to the amplitude to absorb each of the different kinds of polarization (X, Y, Z, T) the photon might be in - technically called the vector and scalar electromagnetic potentials.

In other words, Feynman is claiming to derive classical EM as a particular limit of QED.  Of course that should be possible; the impressive thing here is that, if this approach is indeed what he was referring to in 1966, Feynman felt he could explain it to a "very intelligent person"  (or maybe sufficiently intelligent?).
I should emphasize that "QED" contains no more detail on this topic than what I quoted above.  It's not going to satisfy someone looking for a detailed exposition.  
And maybe his "1966 approach" was something completely different than that of "QED".  Feynman was nothing if not creative.
A: He may have been thinking about teaching physics top-down, rather than bottom-up. There is nothing wrong with that. That's exactly what Landau/Lifshitz do in Volume 1 of their "Course of theoretical physics", by introducing a least action principle and deriving much of Newtonian mechanics from it. One could do the same thing for electrodynamics, but the approach would probably lose many of the lesser gifted students along the way. 
A: Here is a direct link to the section on the Feynman Lectures website that deals with this topic.
BTW, I took a few courses from Feynman and hung out with him a little when he taught at Hughes Aircraft, where I worked at the time.
A BRILLIANT mind and an amazing teacher.
http://www.feynmanlectures.caltech.edu/info/other/Alternate_Way_to_Handle_Electrodynamics.html
A: I found the following quote on the American Institute of Physics website.  It is a continuation of Feynman's quote above.  I believe it answers your question about his new approach.
"When I planned it, I was expected to teach electrodynamics, and then to teach a subject which would really be all the different branches of physics, using the same equation — like you use a diffusion equation for diffusion, for temperature, for lots of things, or the wave equation for sound, for light, and so on. In other words, the second half would have been something like mathematical methods of physics, but with many physics examples, so I’m teaching physics at the same time as the mathematics. I would teach Fourier transform, differential equations, and so on. It wouldn’t look like that, though. It wouldn’t be organized the usual way. It would be in terms of subjects, the point being that the equations are the same in so many different fields. So the moment you deal with an equation, you ought to show all the fields that it comes from, instead of just talking about the equation. So I was going to do that. But then I had another possibility. Maybe I could teach quantum mechanics to the sophomores — nobody expects that to be done, that would be a miracle. And I had a crazy upside down way of presenting quantum mechanics, absolutely inside out, in which everything that was advanced would come first, and everything that was elementary would come, in the conventional sense, last. And I told these guys about that, and they kept working on me. They said I had to do it, that the mathematical thing that I was talking about, other people may someday do, but that this thing would be so unique, and they knew that I would never go for another year. I must do this unique thing, you see — even if it kills the kids, they can’t learn it, and it’s no good. I don’t know what the situation is, actually, whether it’s worthwhile or not. I should try it. So I did. And that’s volume 3 on quantum mechanics. But volumes 2 and 3 were really one year, just like volume 1 was." 
A: It is possible that Feynman was referring to Feynman Diagrams (for which work he received a Nobel Prize).  Feynman diagrams offer a graphical representation of particle interactions collectively known as Quantum Electro Dynamics (QED).  Feynman's contribution provided a means to analyze quite complex interactions without relying solely on manipulating wave equations or matrices.
As an adjunct analysis device, most theoreticians agree that Feynman diagrams have been quite successful.
