Vladimir Hnizdo has now posted a pre-print of a paper that finds, as I did, that angular momentum is not conserved in the spin-orbit interaction:
I'm very happy with this outcome. Not only does it agree with my results, and using an entirely different approach (Lagrangian and Hamiltonian mechanics, which will probably be more convincing to physicists than my cruder methods), and cite my work, but it also shows how the result can be reconciled with the result from quantum theory that angular momentum is conserved in spin-orbit interaction. It turns out, the angular momentum that is constructed using the generalized momentum of Hamiltonian mechanics is conserved. Since quantum mechanics is constructed using the Hamiltonian description, it naturally arrives at the same result of angular momentum conservation. However I think it is nonetheless very important and remarkable that the ordinary angular momentum is not conserved in the spin-orbit interaction.
From a practical standpoint, this should remove a problem I've had in getting published, that no reviewer or journal editor seemingly can get past a statement that angular momentum conservation is violated. I expect that Hnizdo's paper will pass peer review and find publication in a mainstream journal, and at least at that point anyone who disagrees with the angular momentum nonconservation statement can take it up with that journal. I expect that won't happen though because Hnizdo's explanation is very elegant and straightforward and convincing.
In my positronium paper I put on arxiv last December, I lamented explicitly that the problem of angular momentum nonconservation exhibited would cause my entire analysis, which has many other interesting findings, to be disregarded. Now I can thank Vladimir Hnizdo for making it possible for these findings to be fairly examined.
Not messing around
8 hours ago