For this best of calculated, best of tested value, QED is consistent with experimental error, Mills theory is 200X SD wrong.
I just want to remind you that all QED calculations also are based on alpha (and its error) ... But I completely agree that Mills, while doing calculations, sometimes works very sloppy. I never used his alpha for the el-g-factor which in fact is off by a factor of 100 (2 digits) in average. You can do 4D corrections (still a tiny error) but the error/current uncertainty in alpha has the same dimension.
The main problem is that nobody seems to be able to divide out rules for independent measurements of basic constants. I wait for Klitzings next publication about alpha -could take some while. The rubidium measurements are great but you have to believe that they really measure alpha an no other effects interfere...
SM people still believe that the muon is a heavy electron what is utterly wrong. As a consequence the charge radius of the helium is now completely off because the muon is partially repulsive when joining the 4-He orbit. (For proton attractive!)
Such errors are my main concern as THH also confirms that the muon loop is used in the el-g calculations...
As a consequence I focussed my work on deep connections between the best and most reliable measurements in physics world. The more values we can connect the more stable the base will ring to be.
The best mathematical explanation of alpha is De Vries that results in ;
0.00729735256865385/137.0359990958. May be we should use it as long as there is no agreement.