After months of feeling stuck and confused, I have finally been making real progress towards getting my paper on the origin of the magnetic force revised so that I can re-submit to a journal. I saw a different way of going about things, compared to how I was doing it previously, and it really seems to have paid off with new insights.
One new insight is that the force I've been investigating for the last 4 years, the anti-Coriolis force due to Thomas precession of the rest frame of a field-source charged particle as observed from an inertial frame, is not the known magnetic force. The most obvious reason it cannot be the magnetic force is that it vanishes when there is no acceleration of the source particle, whereas the magnetic force needs only a translating, non-accelerating charge to set up a magnetic field that can act on a second translating charge. A second problem is that the force (as described in my paper) has a mass ratio factor, of the ratio of the mass of the particle being acted on to that of the field-source particle, that is not seen in Maxwell-Lorentz electrodynamics. However, due to the fact that most electrodynamical observations are based on electron currents interacting with other electron currents, so that the mass ratio factor would be unity, I was ignoring this problem for the time being. Happily, though, I now believe I have a new understanding of how the magnetic force can arise kinematically as a consequence of Thomas precession, and as an anti-Coriolis force, that does not have these difficulties.
The way around these aforementioned difficulties is to recognize that even if the field-source particle is non-accelerating, because of assumed essentially infinite mass or other constraint (such as being confined to an electrically-neutral wire), its rest frame will undergo Thomas precession from the point of view of a test particle that's being accelerated toward the field-source particle by Coulomb attraction. A physicist-observer in the rest frame of the test particle will notice that although the source particle rest frame is rotating, there is apparently no Coriolis force acting on the test particle in the source particle rest frame, and so deduce that there must be an anti-Coriolis force acting on the test particle there. In this case, however, the numerator mass factor needed in the anti-Coriolis force is cancelled by the denominator mass factor of the same particle acceleration that induces the Thomas precession of the source-particle rest frame. This obtains a magnetic force that agrees with observation in not involving a mass ratio between the field-source and test particles, nor an acceleration of the source particle with respect to an inertial reference frame.
I hope to be able to provide this description quantitatively fairly soon. I will update the paper on arxiv as soon as possible. I may even do a retraction that acknowleges the known problems of the current version and outlines the new approach and findings, in a week or so, prior to posting the full revision. In the meantime, though, I want to mention the new idea I am having about how all of this might relate to the known (so-called) "non-classical" gyromagnetic ratio of the electron. It is of course a well-established fact that the electron produces intrinsic magnetic moment very close to twice as effectively as expected from classical electrodynamics, given its intrinsic angular momentum and charge-to-mass ratio, and assuming it has no complex structure. The idea is, this other force that I've been studying that is the anti-Coriolis force due to Thomas precession of a field-source rest frame when the field-source particle is accelerating under Coulomb attraction or repulsion to the test particle, and a relativistic-kinematics necessity just as is the magnetic force, will effectively double the magnetic field strength for an electron that is generating magnetic moment, at least for one model of the electron spin,. (In the zitterbewegubg model, the electron spin is a consequence of a relativistic circularatory motion of the point charge electron, with radius of the motion equal to the electron Compton wavelength.) Thus the g-factor of two is to be expected, at least according to this model, which I have found compelling for other reasons.