Fermi exclusion principle doesn't look like a fundamental one, rather as effective.

One reason for this principle is Coulomb repulsion between electrons. The popular naive view e.g. on the ground state helium is that it has two independent 1s electrons ... but doing calculations right: using two-electron wavefunction psi(x1,x2) with included electric repulsion, these electrons are strongly anti-correlated: are on the opposite sides on the nucleus. Classical synchronization: http://gryzinski.republika.pl/teor5ang.html

Another argument that 3 electrons would not fit in one orbital is that electrons are tiny magnets. There are only two ways to place two magnets in stable motion: parallel or anti-parallel alignment. Otherwise you would get additional twisting force. While two anti-parallel magnets attract each other (1/r^4) allowing to lower energy (electron can stay closer to nucleus), there is no place for 3 electrons in stable synchronous motion.

Also bosons are only some idealization, e.g. the Bose-Einstein condensate has definitely a nonzero volume, so these are not in the same state.

Regarding energy quantization, see the Couder paper I have linked - orbits are already quantized for classical objects with wave-particle duality. The picture is that to get resonance with the field, particle needs to choose closed orbits, and the the number of ticks of some clock has to be integer while performing this orbit. QM describes such field, but there is also a trajectory of the particle hidden there in Couder's picture, and the same can be true for QM.

This clock is external in Couder, internal for real particles: de Broglies's/zitterbewegung. It was actually observed in experiment, see e.g. Hestenes paper: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.169.7383&rep=rep1&type=pdf