There are two parts to Mills' derivation for quantum states of hydrogen: 1) the part where the principle quantum number has integer values, i.e. n = 1, 2, 3,... 2) the part where the principle quantum number takes on fractional values, i.e. n = 1/2, 1/3, 1/4,..., 1/137.
The first part (i.e. n = 1, 2, 3,...) matches modern quantum theory. Thus part of what you say is true, Mills' results match the Rydberg states. So what? Mills' variation on the mathematics really isn't that cleaver, and if it didn't even match up with observed spectra we wouldn't be talking about it.
The second part is where the problem is. Fractional values for the principle quantum number are provably incorrect from a mathematical (theoretical) basis, and have never been observed in spectra from the sun or anywhere else.
You don't mention Wolfgang Pauli's Exclusion Principle : In a given atom no 2 electrons can have the same n(principle), l(line), m(magnetic) and s(spin) numbers. You defend the n # as only an interger, what about l(line)? Why couldn't the 24 sub-orbitals below the Bohr Radius be LINES, keeping n = 1? You haven't read Dr Mills' work in enough detail, his theory predicts(within a .5% accuracy)the previously unexplained UV lines in the solar spectrum. In a wider view though, what if he's proven right(with working products on the shelf)and you were fighting him tooth and nail all along, what does that do to your reputation as a learned professor?