The non random mechanisms that I suggested can alter multiple nucleotides at the same time
First, when I said that to you before in the context of transposons and gene duplication, you said you were only focusing on single nucleotide mutations. So if we're now back to including mechanisms that can change thousands of bases at a time, then you need to be consistent in your argument.
Second, epigenetics is about changes in gene
expression. It has to do with how genes are "packaged", and isn't a mechanism of mutation. So if we're talking about mutational changes to DNA, you need to drop epigenetics as a mechanism for that.
Natural genetic engineering is available in the peer review literature and as far as I know there are no serious rebuttals.
You seem to be under the impression that if a paper is published in a scientific journal, that means its contents are automatically valid. That's not the case at all. Journals oftentimes publish papers that posit hypotheticals to generate discussion among experts. It's not unusual for those types of papers to either be criticized by the author's peers, or to be ignored and fall into irrelevance.
In Shapiro's case, it was a bit of both. His original paper on NGE was generally ignored, and it wasn't until his book was published that more scientists noticed and offered their criticisms. If you want to see some of them that have been published in scientific journals, go to this Wiki page:
Natural genetic engineering - Wikipedia and read through citations 17-26.
So why wouldn’t it be at pair with epigenetics and transpososn?
Both epigenetics and transposons are directly observed, are relatively well understood, and have been widely accepted for quite a long time. NGE is none of those.