you said this in your paperAs significant progress (relevant to this thread) has been made recently, let me offer a brief followup.
1) My article that I quoted throughout this thread was published in IJQI at last (see the postprint at http://akhmeteli.org/akh-prepr-ws-ijqi2.pdf )
2) The 4th order PDE for one real function, which is generally equivalent to the Dirac equation, was written in an explicit form and published in the Journal of Mathematical Physics (http://akhmeteli.org/wp-content/uploads/2011/08/JMAPAQ528082303_1.pdf )
3) The spinor field was eliminated from the equations of spinor electrodynamics (the Dirac-Maxwell electrodynamics) (with some important caveats), and the results of the IJQI article for scalar electrodynamics were extended to spinor electrodynamics (see http://arxiv.org/abs/1108.1588). One can make different conclusions from these results though: spinor electrodynamics can be replaced by equations for either: a) complex electromagnetic 4-potential, or b) real electromagnetic 4-potential plus one real function (the gradient of which equals the imaginary part of the complex electromagnetic 4-potential of a) ). There is still also a possibility that the above mentioned caveats can be removed altogether, but this has not been proven right or wrong yet.
may be important for interpretation of quantum theory
would you like to tell us about it ?