You make too many assumptions. An ice age doesn't kill everything. Lots of creatures survive just fine in the central tropical area of the earth. You also leave out the possiblity that everything on this earth evolved "de novo". Some may have been "planted" here. Human mitochondrial DNA appears to have a common ancestor that can not be much over 250,000 years old. The Toba volcano appears to have reduced the human population down to around 5,000 individuals. That was around 70,000 years ago.
The author in this post states that the entire Earth was covered in thick ice 105,000 years ago. That simply is not true.
Whether your theory of hypergenerating mitochondrial genes is true or not, the theory that the Earth was completely covered in thick ice 105,000 years ago is just plain wrong.