Thinking about carbon detonation in white dwarf stars (Type IA supernova)

I was reading about white dwarf stars because I've been very interested in neutron stars and I was wondering about something slightly less dense but really still incredibly dense.  While I was reading about that I learned about "Carbon Detonation" in which enough matter falls into a white dwarf star that it causes a runaway fusion reaction and explosion, which we've observed / classified astronomically as type IA supernova.  Here's some thoughts I've had about carbon detonation.

1. matter in white dwarf is very dense - 1e6 g/cm3 - for comparison:
1. water:  1 g/cm3
2. densest metal - osmium:  22 g/cm3
3. center of the earth 12 g/cm3
4. center of the Sun: 150 g/cm3
2. accepted theory is that the "normal" pressure of the plasma is insufficient to prevent further collapse, instead electron degeneracy pressure prevents it
1. simplest model - quantum mechanics particle in a box, as box size decreases energy level spacing increases
3. electron degeneracy pressure only depends on density, not temperature (in contrast to "normal" plasma or gas which depends on both)
4. if mass is added to a white dwarf, density/temperature increases to the point where fusion of carbon and oxygen to heavier elements begins
5. this generates more heat and energy but initially not an increase in volume because the volume is still defined by electron degeneracy
6. this means the energy generated by fusion is not dissipated and the temperature rises rapidly
7. this causes the rate of fusion to increase, causing a positive feedback loop / exponential gain the fusion process
8. This causes the star to explode violently

For matter in a white dwarf - is it a very dense, very hot plasma?  Or is it really something else.  It can crystallize!  E.g. BPM 30793 is a white dwarf that appears to have a crystalline core.

Quick calculation - if it is 1e6 times more dense than water, then the volume per atom is 1e6 smaller in the white dwarf.  That means the spacing between atoms is roughly (1e6)^(1/3) = 1e2 smaller in a white dwarf.  In water it is approximately 3 Å == 3e-10 m, so in a white dwarf it would then be 3e-12m (3 trillionths of a meter).  As a sanity check, the diameter of the carbon nucleus is 2.7e-15 m, so this spacing is bigger than their diameter - by a factor of ~1000.  But still, it is normally 30,000 to 60,000, so this is much compacted.

I can imagine the white dwarf starting as a plasma, cooling to a gas/liquid, then crystallizing to a solid at some point.  It seems that even in the crystalline state there is a fermi sea of electrons - not distinct covalent bonds or ions.  This result was calculated (density functional theory) so it is not measured.  I'm now very curious to see the DFT results as you compress from "normal" density to white dwarf.