Let me explain further, for the electron we have the relationship modolu some constants
k^2 = (E - C/r)^2 - m^2c^4
the non radiation condition ground state us kr=constant so it is wise to study
constant = (rE-C)^2 - r^2m^2c^4
Now essenially rE = rmc^2 + 2C and if rE->nrE=r'E', then
nr'mc^2 + nC = rmc^2 + 2C or
r/n - 2(n-1)C/n/(mc^2) = r'
or r' = r/n aproximately
Now E'r'=E'r/n = nEr => E'=n^2E
Which you can find in GUTCP.
No charge need to be changed, no mass need to be changed.
Note that most likely there are two modulated standing EM waves in the inside (photons) in the QM approach, one related to the mass and one related to the trapped photon and we would then demand that
E_photon r ~n1
E_mass r ~n2
where n1 = 1 for non hydrinos, this as the energy of the mass is of order 1MeV and the energy of the trapped photon is of the order eV. I suspect that the QM approach will never be able to contract the shell to zero width but very thin sop that practically it can be taken such. This explains the higher accuracy of the QM's energy levels and that we can probably deduce a correction that makes the classical approach as exact as the QM's approach. A thing that has bothered me as I do not fancy infinitely thin thingies and QM people bash Mills theory for not being as exact as QM although it is super exact (and QM is super super exact). It seams that via E=mc^2 the mass decides how thin the shell is.