Jerry Coyne's strategies on evolutionary biology

How does Jerry Coyne on his blog respond to (he would probably say "refutes") claims that we need to change the gene-centered neo-Darwinist view of evolution because of epigenetics and other phenomena? Of course there's more than one answer you can find from posts on his blog. But here are a few recurring ones:

1. Ad hominem fallacy: Researchers arguing for the EES and/or a significant role of epigenetic inheritance are biased because they are funded by the Templeton Foundation, whose underlying ideological bias against old-school neo-Darwinism presumably invalidates all research ever funded by them. E.g. "[Proponent of epigenetics Michael] Skinner is eating well from the Templeton trough. It’s pretty clear that Templeton is deeply invested in showing that the “conventional” view of evolution and genetics is wrong, for they’ve also put millions into other researchers to that end."
2. More ad hominems include: researchers being biased to exaggerate their conclusions because they want media attention for their claims of a paradigm shift, papers pushing transgenerational epigenetic inheritance are only published because of stupid biased scientists who have an unshakeable belief in this (presumably nonexistent) process, the media and the public's affinity for epigenetics stories, etc.
3. Epigenetics is still fundamentally under genetic (DNA) control, so DNA-centrism is still valid. E.g. "the position of and influences on a cell can cause it to acquire methylation marks that turn it into difference courses of development: a liver cell, a kidney cell, a bone cell, and so on. But these changes, all inherited among cells in a single body, have resulted from natural selection: they’re adaptive because having different kinds of cells and tissues is adaptive.  What has happened is that the DNA program itself, within the egg, contains information that says “methylate cell X at genes Y and Z if it experiences condition C”, and so on."
4. Epigenetic inheritance doesn't last long enough to cause long-term evolution: "...we have no examples of such acquired methylation lasting more than two or three generations, so there’s no evidence that it could serve as a stable basis of inheritance, much less of adaptation."
5. Studies supposedly showing that such inheritance exists are "...more often than not flawed, relying on p-hacking, small sample sizes, and choosing covariates, like sex, until you get one that shows a significant effect". 

One especially absurd DNA-centric claim Coyne has made which I couldn't believe when I first read it is: "All heritable differences between species, in fact, must reside in the DNA; we know of no cases in which they don’t. Where else could they be?" 

I'm sorry, what? We already know more genes doesn't mean more complexity in organisms, so clearly the differences in gene regulatory networks rather than the genes themselves are what really matter in distinguishing species. Rejecting the idea that genes determine phenotypes is crucial to explaining how humans are different from flies/worms/other organisms w/about the same number of genes. "...the amount of direct genetic information present in, say, the human genome (now estimated to be around 30 000 protein-coding genes) is orders of magnitude below what would be necessary to actually specify the spatial location, functionality and connectivity among the trillions of cells that make up a human brain. The answer must be in the local deployment of information that is possible through developmental processes, where the ‘instructions’ can be used in a way that is sensitive (and therefore capable of adjusting) to both the internal and external environments." Moreover, DNA is not the only biological way (not even counting cultural transmission) for information to be inherited.

OK, so what if 3 is true but 4 is false? "...a methylation-sensing gene regulatory circuit centered on a 5-methylcytosine DNA glycosylase gene is required for long-term epigenetic fidelity in Arabidopsis." So you need DNA to make epigenetics stable across generations. But we see Coyne has created a way to potentially disprove him: you would need to show that epigenetics is stable over "more than two or three generations". Of course he claims no one has done this yet, or if they have it's Templeton-funded p-hacking media-attention-seeking garbage, but is this true? To quote the paper I linked to at the top of this paragraph, "In plants, DNA methylation patterns are faithfully inherited over many generations", and we also know this can happen in yeast too. So clearly Coyne is at least slightly wrong. Sometimes critics of this concept will claim it is valid, but only in non-mammal organisms, a view Coyne seems to share, yet again superficially dismissing studies contradicting this view by collectively accusing them of a smorgasbord of different methodological flaws. But of course he couldn't be bothered to go into detail about what these fatal flaws are in each study.