@THH: The Dirac equation does not include the magnetic energy stored in the field. May be you should ask somebody competent in Maxwell physics to get a better judgement. If QM would include the magnetic energy, the equation are no longer separable, because there is no symmetry between electric forces and magnetic forces.
The even more severe mistake of nuclear physicists is the use of Minkovski space for nuclear models. But that needs an even a more deep understanding of mathematical structures ...
To make is clear: There are some Mathematicians out there, that simply laugh about the math physicists use. But that is unfair, because as an engineering model it often works quite well.
This is not as you have written it clear.
the Dirac equation does not itself include necessary QED calculations. Not surprisingly: we know that QM => virtual particles so total energy now becomes complex, but calculable.
QED is a great theory making precise predictions (even though the calculations are perturbative and necessarily approximate) with wonderful match to experimental data. Mills may claim to have something better than QED. My point is that no-one is competent to say that until, at least, they have a full understanding of QED, unless Mills' stuff is provably more predictive than QED.
I think many people argue something like "QED is complex and weird, some other (easier to understand) must be better". But that is not a true argument. QED is complex computationally and conceptually, but very logically derived from QM (which we know for many other reasons must be true). So the additional complexity of QED - given QM is known - is computational and conceptual but not problematic because there are lots of new assumptions. There is a computational trick to do renormalisation which introduces a parameter, but that parameter can be calculated from multiple different experiments.
My conclusion is the same as that of any experimenter: With Mills I get 3 digits more precision - simply, if I use his rules. Thus: It's not up to me to prove that he is right. The other have to (dis-) prove it.
You'd have to make a comparison with QED and experiment for accuracy. QED is phenomenally accurate for computable cases, and what is computable gets more complex all the time. Furthermore, for the 3 digits from Mills in some cases these are post hoc. Thus Mills is working out how to apply his stuff knowing the correct answer, and his rules are not clearly grounded in other known correct theory - they are free for him to bend to make fit the data. 3 digits could for example come from linear combination of known constituents which might be good enough, but has nothing to do with the specific theory.
If he made predictions provably different than best known values, which turned out after more accurate experiment to be much closer than the best values that would be important and lead one to see that there must be important truth in his stuff. But, remember, that has to be better than the best of the experimental and theoretical from other methods values at any given time. Mills would have these values and would naturally check his results against them and correct errors if his results proved obviously different. You have shown no evidence of Mills actually doing better than figures he could get from others (theoretical or experimental).