This is where you are wrong. MtDNA doesn't recombine and remix. It takes time and it mutates over time, but it only comes from the mother to her children and her fertile daughters will pass it on virtually unchanged for hundreds or thousands of years.
As part of this theory, the hybrid offspring would have to be fertile or mostly fertile and would have to have been preferred mates among the other species of hominins. This could explain the disappearance of their own mtDNA (maternal) lineage.
The nuDNA would remix every generation and would dilute quickly like what we see with Neanderthal nuDNA in modern Europeans. They added a little something to our makeup but there is no trace of Neanderthal mtDNA in human populations, perhaps because those female offspring were infertile or were not preferred mates among male cro magnons ( as you would propose about Patty) or were outcasts and went to stay with the Neanderthals.
Native Americans do tell the stories about abducted women and children, and if true, it could be rare, but ongoing. As I said, it would be a satellite piggy back species that only crosses with us in one direction and keeps the offspring to themselves.
This wouldn't be a comforting thing to unleash on the world, I realize, but unless something in the evidence changes drasticly, like finding Sasquatches true maternal lineage, this is what I have to work with which explains the most evidence in hand.