Alexander,

It seems to me that you have made a Fermionic assumption, or in other words used the Pauli exclusion principle to keep the quanta from overlapping. I rather would have expected a unified field in the singularity that is bosonic and therefore could have overlapping quanta up to Planck energies. Have you calculated the enegy in each quanta when the radius of the singularity approaches the horizon?

Regards,

Richard