No, you did not break quantum mechanics just because the high energy orbitals are more classical in nature. Think about it like so: suppose an electron is barely bound to the hydrogen atom. Suppose there is an EM field at it's ground state with no photons present (we need the field to induce transitions in the hydrogen atom). The electron can now decay to a lower energy state by emitting photons. Because the electron is in such a high quantum level of the hydrogen atom, it can decay by emitting photons of very small energy. To the observer, the emission radiation of a highly excited hydrogen atom gas would look like a continuum at high energies, and therefore these electrons seem to behave classically at temperatures of about ~$10-13 ~\text{eV}$, emitting continuous spectrum radiation and supposedly violating quantum mechanics. 

However, this classical radiation pattern cannot be continued for arbitrarily low energy. Suppose the electron has been emitting small classical looking packets of energy for a while, becoming more and more strongly bound to the hydrogen atom. At some point, given by the resolution of the experiment and the relevant decay times, the experimentalist is going to start seeing radiation only at certain, clearly discrete wavelengths. The electron has become strongly bound again and has lost it's classical character because it came closer to the nucleus, where the transition energies cannot be approximated by a continuum, so they can be deemed classical.

Lesson of the day: Just because something can be approximated as behaving classically in certain regimes of the parameters of the system (high temperature etc.) does not mean it's actually classical. To invoke a theory that doesn't hold in the regime it is to be used to infer results constitutes a logical fallacy.  The correct microscopic theory is decidedly non-classical and it is the one that results like stability of nuclei need to be based on.